For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functio...For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.展开更多
The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has...The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.展开更多
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain t...The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain the nature of supersymmetry in terms of the geometric representation of the wave function and to propose a mechanism of spontaneous symmetry breaking of the excitation of the universe with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitation acquires mass. At the same time, a phase transition of the first kind occurs with the formation of a new phase.展开更多
A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behave...A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.展开更多
The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamenta...The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.展开更多
The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential t...The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.展开更多
The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The cal...The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination.展开更多
The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the ap...The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.展开更多
Shortcomings of the Boltzmann physical kinetics and the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics are considered. From the position of nonlocal p...Shortcomings of the Boltzmann physical kinetics and the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics are considered. From the position of nonlocal physics, the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger equation is a local equation;this fact leads to the great shortcomings of the linear Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics. Nonlocal nonlinear quantum mechanics is considered using the wave function terminology.展开更多
Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result s...Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result shows that the peak of phase shift is the maximum at the atom position as the electron beam along the exact [001] zone axis, and the peak value of phase shift decreases as increases of the misorientation. At small misorientation, i.e. less than 5 degree, change of the phase shift is minimal. The peak value of phase shift decreases significantly when the incident beam deviates form the zone axis over 10 degree and the exit wave has a planar configuration as the misoriention angle arrives -17 degree. The effect of this phase shift characteristics on the information extracted from the hologram has also been considered.展开更多
We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-(ig/2)((1-X2)1/2P + P(1-X2)1/2)...We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-(ig/2)((1-X2)1/2P + P(1-X2)1/2)]|0 in the coordinate representation. A new operator's disentangling formula is derived as a by-product.展开更多
Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologic...Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologically and ontologically considered time dependant momentum operator is initially defined and an Alternative Time Dependant Schrodinger Wave Equation (ATDSWE) is plainly derived. Consequent equation is primarily solved for the free particles, in a closed system, signifying a good agreement with the outcomes of the ordinary TDSWE. Free particle solution interestingly goes further possibly tracing some signs of new pathways to resolve the mysterious quantum world.展开更多
The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum cor...The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.展开更多
We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to ...We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to that in the twodimensional case,the flat band could not survive.At the same time,the flat band states are transformed into localized states with a logarithmic singularity near the center position.In addition,the wave function near the origin would collapse for an arbitrarily weak Coulomb potential.Due to the wave function collapses,the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter.For a Coulomb potential of type II,there exist infinite bound states that are generated from the flat band.Furthermore,when the bound state energy is very near the flat band,the energy is inversely proportional to the natural number,e.g.,E_(n)∝1/n,n=1,2,3,...It is expected that the 1/n energy spectrum could be observed experimentally in the near future.展开更多
By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated r...By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated results show that-the AGP or SPG function gives the same ground state result as their linear combination.展开更多
The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of t...The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of these alkaline spectra enables us to specify the values of these quantum defects. A simple code is used to calculate two quantum defects for which <em>δ<sub>l</sub></em><sub> </sub>can be distinguished as: <em>δ<sub>s</sub></em> <em>l</em> = 0 and <em>δ<sub>p</sub></em> <em>l</em> = 1. On the theoretical part, it is possible to have an analytical expression for these quantum defects <em>δ<sub>l</sub></em>. A second code gives the correct wave functions modified by the quantum defects <em>δ<sub>l</sub></em> with the condition for the principal number: <em>n</em><sub><span style="white-space:nowrap;"><span style="white-space:nowrap;">*</span></span></sub> = <em>n</em> – <em>δ</em><sub><em>l</em></sub> ≥ 1. It is well known that <em>δ</em><sub><em>l</em></sub> → 0 when the kinetic momentum <em>l</em> ≥ 4, and for such momenta the spectra turns out to be hydrogenic. Modern software such as Mathematica, allows us to efficiently generate the polynomes defining wave functions with fractional quantum numbers. This leads to a good theoretical representation of these wave functions. To get numerically the quantum defects, a simple code is given to obtain these quantities when the levels assigned to a transition are known. Then, the quantum defects are inserted into the arguments of the correct modified wave functions for the outer electron of an atom or ion undergoing the short range polarization potential.展开更多
Theoretical and experimental evidences of a causal relation of the phase of the wave function and physical reality are presented. The Copenhagen interpretation of quantum mechanics, which gives physical meaning to the...Theoretical and experimental evidences of a causal relation of the phase of the wave function and physical reality are presented. The Copenhagen interpretation of quantum mechanics, which gives physical meaning to the amplitude of the wave function only, cannot be considered complete on that ground. A new dynamics-statistical interpretation of quantum mechanics is proposed.展开更多
基金supported by the National Key R and D Program of China(2020YFA0713100).
文摘For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.
文摘The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.
文摘The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain the nature of supersymmetry in terms of the geometric representation of the wave function and to propose a mechanism of spontaneous symmetry breaking of the excitation of the universe with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitation acquires mass. At the same time, a phase transition of the first kind occurs with the formation of a new phase.
文摘A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.
文摘The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.
基金the National Natural Science Foundation of China under Grand No.549974011
文摘The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.
文摘The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination.
文摘The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.
文摘Shortcomings of the Boltzmann physical kinetics and the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics are considered. From the position of nonlocal physics, the Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger equation is a local equation;this fact leads to the great shortcomings of the linear Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger wave mechanics. Nonlocal nonlinear quantum mechanics is considered using the wave function terminology.
基金financially supported tional Natural Science Foundation of China No. 60271028.
文摘Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result shows that the peak of phase shift is the maximum at the atom position as the electron beam along the exact [001] zone axis, and the peak value of phase shift decreases as increases of the misorientation. At small misorientation, i.e. less than 5 degree, change of the phase shift is minimal. The peak value of phase shift decreases significantly when the incident beam deviates form the zone axis over 10 degree and the exit wave has a planar configuration as the misoriention angle arrives -17 degree. The effect of this phase shift characteristics on the information extracted from the hologram has also been considered.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)
文摘We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-(ig/2)((1-X2)1/2P + P(1-X2)1/2)]|0 in the coordinate representation. A new operator's disentangling formula is derived as a by-product.
文摘Time evaluation of wave functions for any quantum mechanical system/particle is essential nevertheless quantum mechanical counterpart of the time dependant classical wave equation does simply not appear. Epistemologically and ontologically considered time dependant momentum operator is initially defined and an Alternative Time Dependant Schrodinger Wave Equation (ATDSWE) is plainly derived. Consequent equation is primarily solved for the free particles, in a closed system, signifying a good agreement with the outcomes of the ordinary TDSWE. Free particle solution interestingly goes further possibly tracing some signs of new pathways to resolve the mysterious quantum world.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974229 and 11274215)。
文摘The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.
基金the supports of startup grant from Guangzhou Universitysupported by the National Natural Science Foundation of China(Grant No.11874127)。
文摘We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to that in the twodimensional case,the flat band could not survive.At the same time,the flat band states are transformed into localized states with a logarithmic singularity near the center position.In addition,the wave function near the origin would collapse for an arbitrarily weak Coulomb potential.Due to the wave function collapses,the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter.For a Coulomb potential of type II,there exist infinite bound states that are generated from the flat band.Furthermore,when the bound state energy is very near the flat band,the energy is inversely proportional to the natural number,e.g.,E_(n)∝1/n,n=1,2,3,...It is expected that the 1/n energy spectrum could be observed experimentally in the near future.
基金Supported by the National Natural Science Foundation of China
文摘By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated results show that-the AGP or SPG function gives the same ground state result as their linear combination.
文摘The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of these alkaline spectra enables us to specify the values of these quantum defects. A simple code is used to calculate two quantum defects for which <em>δ<sub>l</sub></em><sub> </sub>can be distinguished as: <em>δ<sub>s</sub></em> <em>l</em> = 0 and <em>δ<sub>p</sub></em> <em>l</em> = 1. On the theoretical part, it is possible to have an analytical expression for these quantum defects <em>δ<sub>l</sub></em>. A second code gives the correct wave functions modified by the quantum defects <em>δ<sub>l</sub></em> with the condition for the principal number: <em>n</em><sub><span style="white-space:nowrap;"><span style="white-space:nowrap;">*</span></span></sub> = <em>n</em> – <em>δ</em><sub><em>l</em></sub> ≥ 1. It is well known that <em>δ</em><sub><em>l</em></sub> → 0 when the kinetic momentum <em>l</em> ≥ 4, and for such momenta the spectra turns out to be hydrogenic. Modern software such as Mathematica, allows us to efficiently generate the polynomes defining wave functions with fractional quantum numbers. This leads to a good theoretical representation of these wave functions. To get numerically the quantum defects, a simple code is given to obtain these quantities when the levels assigned to a transition are known. Then, the quantum defects are inserted into the arguments of the correct modified wave functions for the outer electron of an atom or ion undergoing the short range polarization potential.
文摘Theoretical and experimental evidences of a causal relation of the phase of the wave function and physical reality are presented. The Copenhagen interpretation of quantum mechanics, which gives physical meaning to the amplitude of the wave function only, cannot be considered complete on that ground. A new dynamics-statistical interpretation of quantum mechanics is proposed.