Wavefunctions for Particles with arbitrary Spin

By solving rigorously the relativistic wave equations derived from Bargmann–Wigner equation for arbitrary spin, the relativistic wavefunctions in momentum representation for particles with arbitrary spin are deduced.

WAVEFUNCTIONS OF L-S COUPLING FERMION SYSTEM(Ⅰ): SINGLE-l

In this paper. it is discussed how to constrnct wavefunctions of L-S couplingfermion system, which are classified by group chain A recurrent formula of fractional parentage coefficients with fixedseniority is also given.

WAVEFUNCTIONS OF L-S COUPLING FERMION SYSTEM (Ⅱ):DOUBLE■-l

The wavefunctions of L-S coupling fermion system, which are classified by group chain U(4ι1 + 4ι2 + 4) Us(2)×(U L(2ι+ 2ι2 + 2) O(2ι1 + 2ι2 + 2) O(2ι+1) ×O(2ι2 + 1) O1 (3)×O2 (3) O(3)), are constructed through introducing generalized pairs coupled by fermions with different ι. With the help of the fractional parentage coefficients of single-ιfermion system, the author obtains the corresponding fractional parentage coefficients of double-ιfermion system.

Digital holographic imaging via direct quantum wavefunction reconstruction

Wavefunction is a fundamental concept of quantum theory.Recent studies have shown surprisingly that wavefunction can be directly reconstructed via the measurement of weak value.The weak value based direct wavefunction reconstruction not only gives the operational meaning of wavefunction,but also provides the possibility of realizing holographic imaging with a totally new quantum approach.Here,we review the basic background knowledge of weak value based direct wavefunction reconstruction combined with recent experimental demonstrations.The main purpose of this work focuses on the idea of holographic imaging via direct wavefunction reconstruction.Since research on this topic is still in its early stage,we hope that this work can attract interest in the field of traditional holographic imaging.In addition,the wavefunction holographic imaging may find important applications in quantum information science.

Energy levels and states of parabolic cylindrical lens shaped quantum dots

The parabolic cylindrical lens shaped quantum dot is investigated theoretically. The Schrǒdinger equation for an electron confined in this structure is solved in the parabolic cylindrical coordinate system. The wavefunctions for the electron are presented in terms of confluent hypergeometric functions, and the electron energy spectra are also obtained.

Strength of Intramolecular Hydrogen Bonds

The concept of resonance-assisted hydrogen bonds(RAHBs)highlights the synergistic interplay between theπ-resonance and hydrogen bonding interactions.This concept has been well-accepted in academia and is widely used in practice.However,it has been argued that the seemingly enhanced intramolecular hydrogen bonding(IMHB)in unsaturated compounds may simply be a result of the constraints imposed by theσ-skeleton framework.Thus,it is crucial to estimate the strength of IMHBs.In this work,we used two approaches to probe the resonance effect and estimate the strength of the IMHBs in the two exemplary cases of the enol forms of acetylacetone and o-hydroxyacetophenone.One approach is the block-localized wavefunction(BLW)method,which is a variant of the ab initio valence bond(VB)theory.Using this approach,it is possible to derive the geometries and energetics with resonance shut down.The other approach is Edmiston’s truncated localized molecular orbital(TLMO)technique,which monitors the energy changes by removing the delocalization tails from localized molecular orbitals.The integrated BLW and TLMO studies confirmed that the hydrogen bonding in these two molecules is indeed enhanced byπ-resonance,and that this enhancement is not a result ofσconstraints.

Wavefunction and energy of the 1s^2 2sns configuration in a beryllium atom

A new set of trial functions for 1s^22sns configurations in a beryllium atom is suggested. A Mathematica program based on the variational method is developed to calculate the wavefunctions and energies of 1s^22sns （n = 3 - 6） configurations in a beryllium atom. Non-relativistic energy, polarization correction and relativistic correction which include mass correction, one- and two-body Darwin corrections, spin-spin contact interaction and orbit-orbit interaction, are calculated respectively. The results are in good agreement with experimental data.

Magneto-optical properties of self-assembled InAs quantum dots for quantum information processing

Semiconductor quantum dots have been intensively investigated because of their fundamental role in solid-state quan- tum information processing. The energy levels of quantum dots are quantized and can be tuned by external field such as optical, electric, and magnetic field. In this review, we focus on the development of magneto-optical properties of single InAs quantum dots embedded in GaAs matrix, including charge injection, relaxation, tunneling, wavefunction distribution, and coupling between different dimensional materials. Finally, the perspective of coherent manipulation of quantum state of single self-assembled quantum dots by photocurrent spectroscopy with an applied magnetic field is discussed.

Modified Atomic Orbital Calculations of Energy of the(2s^(2)^(1)S)Ground-State,the(2p^(2)^(1)D);(3d^(2)^(1)G)and(4f^(2)^(1)I)Doubly Excited States of Helium Isoelectronic Sequence from H-to Ca^(18+)

We report in this paper the ground-state energy 2s^(2)^(1)S and total energies of doubly excited states 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I of the Helium isoelectronic sequence from H-to Ca^(18+).Calculations are performed using the Modified Atomic Orbital Theory(MAOT)in the framework of a variational procedure.The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function[1]combining with Hylleraas-type wave function[2].The study leads to analytical expressions which are carried out under special MAXIMA computational program.This first proposed MAOT variational procedure,leads to accurate results in good agreement as well as with available other theoretical results than experimental data.In the present work,a new correlated wave function is presented to express analytically the total energies for the 2s21S ground state and each doubly 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the(nI^(2))systems.

Separation of Variable Treatment for Solving Time—Dependent Potentials

We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.

Incoherent control of two classes of finite-level quantum systems

The incoherent control of finite-level quantum systems is investigated. Following a brief introduction to coherent control paradigms in quantum control, a control problem that can not be accomplished using only coherent control is presented. For such a control problem, it is proved that it can be accomplished using incoherent control based on projective measurement and coherent control for two classes of finite-level quantum systems, i.e., eigenstate controllable quantum systems and wavefunction controllable quantum systems.

Evaluating First-Order Molecular Properties of Delocalized Ionic or Excited States in Molecular Aggregates by Renormalized Excitonic Method

In the past few years,the renormalized excitonic model(REM)approach was developed as an efficient low-scaling ab initio excited state method,which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings.In this work,we further extend the REM calculations for the evaluations of first-order molecular properties(e.g.charge population and transition dipole moment)of delocalized ionic or excited states in molecular aggregates,through generalizing the effective Hamiltonian theory to effective operator representation.Results from the test calculations for four different kinds of one dimensional(1D)molecular aggregates(ammonia,formaldehyde,ethylene and pyrrole)indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.

The impact of vibrational wave function on low energy electron vibrational scattering from nitrogen molecule

The vibrational wave function of the target theoretically plays an important role in the calculation of vibrational excitation cross sections. By a careful study of the differential cross sections resulting from different vibrational wave functions we find that cross sections are susceptible to vibrational wave functions. Minor changes in the vibration wave lhnction may cause a significant change in the cross section. Even more surprising is that by selecting a few numbers of potential models （which determine the vibrational wave functions） we can often calculate the differential scattering cross section in much closer agreement with experiment in the framework of body-frame vibrational close-coupling theory, which suggest that an accurate potential energy may play a more important role in scattering than we thought betbre.

Hidden Anderson localization in disorder-free Ising–Kondo lattice

Anderson localization (AL) phenomena usually exist in systems with random potential. However, disorder-free quantum many-body systems with local conservation can also exhibit AL or even many-body localization transition. We show that the AL phase exists in a modified Kondo lattice without external random potential. The density of state, inverse participation ratio and temperature-dependent resistance are computed by classical Monte Carlo simulation, which uncovers an AL phase from the previously studied Fermi liquid and Mott insulator regimes. The occurrence of AL roots from quenched disorder formed by conservative localized moments. Interestingly, a many-body wavefunction is found, which captures elements in all three paramagnetic phases and is used to compute their quantum entanglement. In light of these findings, we expect that the disorder-free AL phenomena can exist in generic translation-invariant quantum many-body systems.

A New Form for the Full Salpeter Equation

A more general form of the Bethe Salpater wavefunction for a quark antiquark bound state, in accordance with the spirit of nonrelativistic approximation, is constructed, and the relativistic Salpeter equation is reduced to two 2×2 matrix equations under an instantaneous approximation, which includes not only the contributions comming from a positive energy state but also ones of a negative energy state, and has no anomalous solution.

Analytical Study of Band Structure of Material Using Relativistic Concept

In this paper, we present the study of band structure relativistically. Here, Dirac equation is formulated from Hamilto-nian in which the formulation is found to contain a correction term known as spin-orbit coupling given as that modifies the non-relativistic expression for the same formulation. This term leads to double spin-degeneracy within the first Brillioun zone which is a concept that is not found in other method of study of band structure of material.

On the Interpretation of the Foundations of Quantum Mechanics

This study discusses the information space, the wave function phase, the Berry phase and its relationship to quantization, discriminability of states and macroscopic quantum effects caused by localization of the particle, followed by a possible entropy change during its transition into a new thermodynamic state. This work addresses interference： it is the information waves which interfere; the particles follow their roadmap, and the measurement of their coordinates introduces an additional uncertainty into the momentum. It is not particles （matter） which manifest these wave properties but fluctuations of the physical space-time coordinates. Physical characteristics corresponding to the fluctuating variables, energy, momentum, etc., determine the magnitude of the respective fluctuations rather than the wave properties of matter. Matter possesses no wave properties. This work also discusses the difference between the objective information and knowledge.

Investigating Initial Conditions of the WdW Equation in Flat Space in a Transition from the Pre-Planckian Physics Era to the Electroweak Regime of Space-Time

This document is due to reviewing an article by Maydanyuk and Olkhovsky, of a Nova Science conpendium as of “The big bang, theory assumptions and Problems”, as of 2012, which uses the Wheeler De Witt equation as an evolution equation assuming a closed universe. Having the value of k, not as the closed universe, but nearly zero of a nearly flat universe, which leads to serious problems of interpretation of what initial conditions are. These problems of interpretations of initial conditions tie in with difficulties in using QM as an initial driver of inflation. And argue in favor of using a different procedure as far as forming a wave function of the universe initially. The author wishes to thank Abhay Ashtekar for his well thought out criticism but asserts that limitations in space-time geometry largely due to when is formed from semi classical reasoning, i.e. Maxwell’s equation involving a close boundary value regime between Octonionic geometry and flat space non Octonionic geometry is a datum which Abhay Ashekhar may wish to consider in his quantum bounce model and in loop quantum gravity in the future.

Wrong Potential Energy Term in Schrödinger’s Equation for Hydrogen Atom

Even after nine decades of successful run of the Quantum Mechanics (QM), different viewpoints on foundational problems of Quantum Physics are still being actively debated. That is because mathematical logic of QM often defies the physical intuition which constitutes the main spirit of Physics. De Broglie’s hypothesis of matter waves implied that the dynamic characteristics of a micro particle in motion, can be ascribed to the wave characteristics of the wavelet accompanying the particle. The Schrödinger equation models the matter-wave interactions through wavefunction ψ?and effectively serves as the foundation of QM. Even though mathematical structure of the Schrödinger equation is sound and elegant, here we show a conceptual mistake in the development of this equation wherein the physical situation has not been correctly modeled in the equation. The Coulomb potential energy of the proton electron pair in Hydrogen atom is essentially the negative interaction energy between their superposed electrostatic fields which is inversely proportional to their instantaneous separation distance. Assuming the proton to be relatively fixed at the origin of an appropriate coordinate system, the potential energy of the orbiting electron will be a function of instantaneous position coordinates of the electron. This has not been properly modeled in the Schrödinger equation. The resulting errors in the solution have been quantitatively demonstrated in this paper. We have stressed the necessity of incorporating a specific correction in the potential energy term of the Schrödinger equation, after which it may facilitate the adoption of Bohmian QM.