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On the Relativistic Harmonic Oscillator
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作者 Yair Zarmi 《Applied Mathematics》 2023年第1期1-20,共20页
The relativistic harmonic oscillator represents a unique energy-conserving oscillatory system. The detailed characteristics of the solution of this oscillator are displayed in both weak- and extreme-relativistic limit... The relativistic harmonic oscillator represents a unique energy-conserving oscillatory system. The detailed characteristics of the solution of this oscillator are displayed in both weak- and extreme-relativistic limits using different expansion procedures, for each limit. In the weak-relativistic limit, a Normal Form expansion is developed, which yields an approximation to the solution that is significantly better than in traditional asymptotic expansion procedures. In the extreme-relativistic limit, an expansion of the solution in terms of a small parameter that measures the proximity to the limit (v/c) &#8594;1 yields an excellent approximation for the solution throughout the whole period of oscillations. The variation of the coefficients of the Fourier expansion of the solution from the weak- to the extreme-relativistic limits is displayed. 展开更多
关键词 Relativistic harmonic oscillator Weak-Relativistic Limit Extreme-Relativistic Limit
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Loop Quantum Gravity Harmonic Oscillator
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作者 Edwin Eugene Klingman 《Journal of Modern Physics》 2023年第9期1287-1303,共17页
Attempts to unify Gravity Theory and Quantum Field Theory (QFT) under Loop Quantum Gravity Theory (LQG), are diverse;a dividing line between classical and quantum is sought with Schrödinger cat-state experiments.... Attempts to unify Gravity Theory and Quantum Field Theory (QFT) under Loop Quantum Gravity Theory (LQG), are diverse;a dividing line between classical and quantum is sought with Schrödinger cat-state experiments. A Primordial Field Theory-based alternative is presented, and a gravity-based harmonic oscillator developed. With quantum theory applied at micro-scales and gravity theory at meso- and macro-scales, this scale-gap contributes to the conceptual problems associated with Loop Quantum Gravity. Primordial field theory, spanning all scales, is used to conceptually stretch key ideas across this gap. An LQG interpretation of the wave function associated with the oscillator is explained. 展开更多
关键词 Quantum Loop Gravity Spacetime Ontology Energy-Time Ontology harmonic oscillator MESO-SCALE Cat States Gravitational Wave Function
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A Model Effective Mass Quantum Anharmonic Oscillator and Its Thermodynamic Characterization
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作者 M. Vubangsi F. B. Migueu +3 位作者 B. F. Kamsu L. S. Yonya Tchapda M. Tchoffo L. C. Fai 《Journal of Applied Mathematics and Physics》 2021年第2期306-316,共11页
Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the ... Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges. 展开更多
关键词 Ordering Ambiguity Anharmonicity Parameter Variable Mass Anharmonic oscillator Thermodynamic Resonance Complex Entropy Quantum harmonic oscillator
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Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp(4,R) Lie Algebra 被引量:1
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作者 PANFeng DAILian-Rong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2001年第6期661-664,共4页
Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determi... Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2). 展开更多
关键词 coupled harmonic oscillators Sp(4 R) Lie algebra vector coherent states
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Sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays 被引量:1
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作者 Jin Zhou Hua Zhang +1 位作者 Lan Xiang Quanjun Wu 《Theoretical & Applied Mechanics Letters》 CAS 2013年第6期15-19,共5页
In this letter, a distributed protocol for sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays is proposed, and a brief procedure of convergence analysis for s... In this letter, a distributed protocol for sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays is proposed, and a brief procedure of convergence analysis for such algorithm over undirected connected graphs is provided. Furthermore, a simple yet generic criterion is also presented to guarantee synchronized oscillatory motions in coupled harmonic oscillators. Subsequently, the simulation results are worked out to demonstrate the efficiency and feasibility of the theoretical results. 展开更多
关键词 sampled-data synchronization coupled harmonic oscillators controller failure communi-cation delays
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Noncovariant Lagrangians Are Presented Which Yield Two-Component Equations of Motion for a Class of Relativistic Mechanical Systems in 1 + 1 Dimensions Including the Harmonic Oscillator 被引量:1
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作者 Robert L. Anderson 《Applied Mathematics》 2020年第9期917-921,共5页
First, a Lagrangian is presented and authenticated for a Relativistic Harmonic Oscillator in 1 + 1 dimensions. It yields a two-component set of equations of motion. The time-component is the missing piece in all previ... First, a Lagrangian is presented and authenticated for a Relativistic Harmonic Oscillator in 1 + 1 dimensions. It yields a two-component set of equations of motion. The time-component is the missing piece in all previous discussions of this system! The second result is that this Oscillator Langrangian generalizes to Langrangians for a class of particles in 1 + 1 dimensions subject to an arbitrary potential <em>V</em> which is space dependent only. 展开更多
关键词 harmonic oscillator
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Stochastic Resonance in a Harmonic Oscillator Fluctuating Intrinsic Frequency by Asymmetric Dichotomous Noise 被引量:1
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作者 Shi-Qi Jiang Bo Wu Tian-Xiang Gu 《Journal of Electronic Science and Technology of China》 2007年第4期344-347,共4页
The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov ... The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov formula, the exact solution of the average output amplitude gain (OAG) is obtained. Numerical results show that OAG depends non-monotonically on the noise characteristics: intensity, correlation time and asymmetry. The maximum OAG can be achieved by tuning the noise asymmetry and or the noise correlation time. 展开更多
关键词 Asymmetric dichotomous noise harmonic oscillator output amplitude gain stochastic resonance.
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Variable Frequency Harmonic Oscillator in an Electromagnetic Field
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作者 HUANGBo-Wen WANGJing-Shan +1 位作者 GUZhi-Yu QIANShang-Wu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第1期45-47,共3页
The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space p... The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method. The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field are obtained. 展开更多
关键词 INVARIANT PROPAGATOR canonical transformation phase space path integral variable frequency harmonic oscillator
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Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency
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作者 Lei Jiang Li Lai +1 位作者 Tao Yu Maokang Luo 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第6期176-187,共12页
The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condi... The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears. 展开更多
关键词 coupled harmonic oscillators dichotomous fluctuating frequency SYNCHRONIZATION stability stochastic resonance
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Anomalous Dissipative Quantum Harmonic Oscillator
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作者 BAI Zhan-Wu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第1期137-142,共6页
We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low... We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators' spectral density, the coordinate and momentum correlation functions decay as T^-4 arid T^-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case. 展开更多
关键词 harmonic oscillator harmonic velocity noise zero point energy correlation function the thirdlaw of thermodynamics
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Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity
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作者 HUANGBo-Wen QIANShang-Wu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2003年第2期155-156,共2页
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
关键词 force quadratic in velocity time-dependent damped harmonic oscillator coordinate transformation method of time-dependent invariant PROPAGATOR
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Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State
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作者 唐绪兵 许雪芬 范洪义 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第7期67-72,共6页
For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integrationoperator in coherent state representation and then perform this integral by virtue of the technique of integ... For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integrationoperator in coherent state representation and then perform this integral by virtue of the technique of integration withinan ordered product of operators.The normally ordered time evolution operator is thus obtained.We then derive theWigner function of u(t)|n>,where |n> is a Fock state,which exhibits a generalized squeezing,the squeezing effect isrelated to the varying mass with time. 展开更多
关键词 harmonic oscillator Wigner function damping mass-varying
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Forced Time-Dependent Harmonic Oscillators in Non-Commutative Space
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作者 LIANG Mai-Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第3期410-414,共5页
For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld inva... For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space. 展开更多
关键词 non-commutative quantum mechanics harmonic oscillator geometric phase coherent state
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Quantum and Classical Exact Solutions of Harmonic Oscillator in a Time-Dependent Magnetic Field
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作者 LIANGMai-Lin LIULi-Yan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6期1027-1029,共3页
In cylindrical coordinate, exact wave functions of the two-dimensional time-dependent harmonic oscillator in a time-dependent magnetic field are derived by using the trial function method. Meanwhile, the exact classic... In cylindrical coordinate, exact wave functions of the two-dimensional time-dependent harmonic oscillator in a time-dependent magnetic field are derived by using the trial function method. Meanwhile, the exact classical solution as well as the classicalphase is obtained too. Through the Heisenberg correspondence principle, the quantum solution and the classical solution are connected together. 展开更多
关键词 harmonic oscillator magnetic field exact wave function exact classicalsolution
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Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries
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作者 C.F.Lo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第11期820-824,共5页
By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrodinger equation describing a... By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrodinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special eases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time- dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. 展开更多
关键词 infinite square well harmonic oscillator moving boundaries Fourier series
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Generalized Harmonic Oscillator and the Schrdinger Equation with Position-Dependent Mass
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作者 JU Guo-Xing CAI Chang-Ying REN Zhong-Zhou 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第5期797-802,共6页
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue a... We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator. 展开更多
关键词 generalized harmonic oscillator Schr6dinger equation position-dependent mass coherent state
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Generalized Fourth-Order Decompositions of Imaginary Time Path Integral:Implications of the Harmonic Oscillator
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作者 Cong Wang Lihan Zhang +1 位作者 Jian Liu Jiushu Shao 《Chinese Journal of Chemical Physics》 SCIE EI CAS CSCD 2022年第3期516-536,I0003,共22页
The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they... The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems. 展开更多
关键词 Path integral DECOMPOSITION Partition function harmonic oscillator
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Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation
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作者 QIAN Shang-Wu WANG Jing-Shan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期308-310,共3页
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-... A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived. 展开更多
关键词 gauge-invariant formulation of non-relativistic quantum mechanics time-dependent harmonic oscillator magnetic dipole approximation gauge-invariant transition probability amplitude
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Calculation of Gaussian Perturbation on Two Harmonic Oscillators by Virtue of Entangled State Representation
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作者 HU Li-Yun ZHOU Nan-Run FAN Hong-Yi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第4X期629-632,共4页
The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state repr... The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state representation. It turns out that the matrix elements are just related to Gegenbauer polynomial and Hypergeometric function respectively. The 1st- and 2nd-order corrections to the energy levels and the 1st-order correction to wave functions of harmonic oscillator are deduced. 展开更多
关键词 harmonic oscillator Gaussian perturbation IWOP technique
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Strategies for h-Adaptive Refinement for a Finite Element Treatment of Harmonic Oscillator Schrodinger Eigenproblem
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作者 T.D.Young R.Armiento 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第6期1017-1023,共7页
A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two comp... A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver. 展开更多
关键词 adaptive finite element analysis harmonic oscillator problems Schrodinger equation
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