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The fractional features of a harmonic oscillator with position-dependent mass

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Communications in Theoretical Physics 2020年第5期72卷 13-20页

作者： Dumitru Baleanu Amin Jajarmi Samaneh Sadat Sajjadi H Asad Department of Mathematics Faculty of Arts and SciencesCankaya University06530 AnkaraTurkey Institute of Space Sciences PO Box MG–23R 76900Magurele–BucharestRomania Department of Electrical Engineering University of BojnordPO Box 94531–1339BojnordIran Department of Electrical and Computer Engineering Hakim Sabzevari UniversitySabzevarIran Palestine Technical University College of Arts and SciencesDepartment of PhysicsPO Box 7 TulkarmPalestine

In this study,a harmonic oscillator with position-dependent mass is ***,as an introduction,we give a full description of the system by constructing its classical Lagrangian;thereupon,we derive the related classical equations of motion such as the classical Euler–Lagrange ***,we fractionalize the classical Lagrangian of the system,and then we obtain the corresponding fractional Euler–Lagrange equations(FELEs).As a final step,we give the numerical simulations corresponding to the FELEs within different fractional *** results based on the Caputo and the Atangana-Baleanu-Caputo(ABC)fractional derivatives are given to verify the theoretical analysis.

关键词： position-dependent mass harmonic oscillator Euler–Lagrange equations fractional derivative

Coherent States and Uncertainty Product of the harmonic oscillator with Position-Dependent Mass

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Journal of Quantum Information Science 2022年第1期12卷 13-20页

作者： Chadia Qotni Hicham Laribou Departement des Sciences Ecole Normale Supérieure University Moulay Ismail Meknès Morocco Laboratoire de Microstructure et de Mécanique des Matériaux Université de Lorraine Metz France

In this work, we applied the invariant method to calculate the coherent state of the harmonic oscillator with position-dependent mass, which in modern physics has great application. We also obtain the calculation of H... 详细信息

关键词： Schrodinger Equation Wave Function Coherent State harmonic oscillator Position Dependent Mass

Bound states of the Klein-Gordon and Dirac equations for scalar and vector harmonic oscillator potentials

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Chinese Physics B 2002年第8期11卷 757-758页

作者： Qiang Wen-Chao(强稳朝) Faculty of Science Xi'an University of Architecture and Technology Xi'an 710055 China

We give the exact bound states of the Klein-Gordon and Dirac equations with equal scalar and vector harmonicoscillator potentials.

关键词： harmonic oscillator Klein-Gordon equation Dirac equation bound state

Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

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Chinese Physics B 2005年第6期14卷 1075-1076页

作者：陈刚 Departmentofphysics ShaoxingCollegeofArtsandSciencesShaoxing312000China//MaterialsPhysicsandEquipmentsInstituteofShaoxingUniversityShaoxing312000China

The N-dimensional Schrodinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method of solving Schrodinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.

关键词： bound state harmonic oscillator Laplace transformation

Stochastic Resonance in a harmonic oscillator Fluctuating Intrinsic Frequency by Asymmetric Dichotomous Noise

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Journal of Electronic Science and Technology of China 2007年第4期5卷 344-347页

作者： Shi-Qi Jiang Bo Wu Tian-Xiang Gu School of Automation Engineering University of Electronic Science and Technology of China （UESTC） Chengdu 610054China China Gas Turbine Establishment Chengdu 610500 China School of Automation Engineering University of Electronic Science and Technology of China Chengdu 610054 China

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.

关键词： Asymmetric dichotomous noise harmonic oscillator output amplitude gain stochastic resonance.

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

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Applied Mathematics 2020年第9期11卷 917-921页

作者： Robert L. Anderson Department of Physics and Astronomy University of Georgia Athens Georgia USA

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 V which is space dependent only.

关键词： harmonic oscillator

Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

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Journal of Modern Physics 2024年第4期15卷 474-479页

作者： Gustavo V. López Jorge A. Lizarraga Departamento de Física Universidad de Guadalajara Guadalajara Mexico

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

关键词： Gauge Transformation harmonic oscillator Quantum Hall Effect Electromagnetic Potentials

Connes distance of 2D harmonic oscillators in quantum phase space

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Chinese Physics B 2021年第11期30卷 170-179页

作者：林冰生衡太骅 School of Mathematics South China University of TechnologyGuangzhou 510641China Laboratory of Quantum Science and Engineering South China University of TechnologyGuangzhou 510641China School of Physics and Material Science Anhui UniversityHefei 230601China

We study the Connes distance of quantum states of two-dimensional(2D)harmonic oscillators in phase *** the Hilbert–Schmidt operatorial formulation,we construct a boson Fock space and a quantum Hilbert space,and obtain the Dirac operator and a spectral triple corresponding to a four-dimensional(4D)quantum phase *** on the ball condition,we obtain some constraint relations about the optimal *** construct the corresponding optimal elements and then derive the Connes distance between two arbitrary Fock states of 2D quantum harmonic *** prove that these two-dimensional distances satisfy the Pythagoras *** results are significant for the study of geometric structures of noncommutative spaces,and it can also help us to study the physical properties of quantum systems in some kinds of noncommutative spaces.

关键词： Connes distance noncommutative geometry harmonic oscillator

Synchronization of instantaneous coupled harmonic oscillators with local interaction

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Synchronization of instantaneous coupled harmonic oscillator...