Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

DOI10.1016/j.aop.2015.07.022zbMath1343.81073arXiv1502.05333OpenAlexW1004626263MaRDI QIDQ307547

J. C. Sandoval-Santana, J. L. Cardoso, V. G. Ibarra-Sierra, Alejandro Kunold

Publication date: 2 September 2016

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.05333

zbMATH Keywords

Lie algebraevolution operatorquantum harmonic oscillatorcharged particle in electromagnetic fieldsion trapmicrowave induced magnetoresistance oscillations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie (super)algebras to physics, etc. (17B81) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items

Exact time-evolution of a generalized two-dimensional quantum parametric oscillator in the presence of time-variable magnetic and electric fields ⋮ Study of time evolution for approximation of two-body spinless Salpeter equation in presence of time-dependent interaction ⋮ Quasienergy operators and generalized squeezed states for systems of trapped ions ⋮ Method for Finding the Exact Effective Hamiltonian of Time‐Driven Quantum Systems ⋮ Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator ⋮ Squeezed coherent states of motion for ions confined in quadrupole and octupole ion traps ⋮ Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

Cites Work

• Exact linear invariants and quantum effects in the early Universe
• On the quantum motion of a generalized time-dependent forced harmonic oscillator
• The time-dependent quantum harmonic oscillator revisited: Applications to quantum field theory
• Coherent-state propagator of two coupled generalized time-dependent parametric oscillators.
• On the squeezing of coherent light coupled to a driven damped harmonic oscillator with time dependent mass and frequency
• Solution to the Schrödinger equation for the time-dependent potential
• Quantum and classical dissipation of charged particles
• Lewis-Riesenfeld approach to the solutions of the Schrödinger equation in the presence of a time-dependent linear potential
• On the algebraic approach to the time-dependent quadratic Hamiltonian
• Path integral evaluation of the Bloch density matrix for an oscillator in a magnetic field
• The evolution operator technique in solving the Schrodinger equation, and its application to disentangling exponential operators and solving the problem of a mass-varying harmonic oscillator
• On Dissipative Systems and Related Variational Principles
• Quantum motion in a Paul trap
• Exact Quantization Conditions. II
• Lie Algebraic Solution of Linear Differential Equations
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
• On the exponential solution of differential equations for a linear operator
• The quantum damped harmonic oscillator

This page was built for publication: Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields