Journal ArticleDOI
Exact wave functions of a harmonic oscillator with time-dependent mass and frequency
TLDR
In this paper, the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency were obtained using the Lewis and Riesenfeld invariant method.Abstract:
We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] to obtain the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency. Exact coherent states for such system are also constructed.read more
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The quantum damped harmonic oscillator
TL;DR: In this article, the authors show that the path integral method yields the exact quantum theory of the Caldirola-Kanai Hamiltonian without violation of Heisenberg's uncertainty principle.
Journal ArticleDOI
Path Integral Formulation of Fractionally Perturbed Lagrangian Oscillators on Fractal
TL;DR: In this article, a fractional path integral for harmonic oscillators characterized by a perturbed Lagrangian was developed based on the framework of the fractional action-like variational approach.
Journal ArticleDOI
Exact time dependence of solutions to the time-dependent Schrödinger equation
TL;DR: In this article, the Schrodinger equation with an exact time dependence is derived as eigenfunctions of dynamical invariants which are constructed from time-independent operators using time-dependent unitary transformations.
Journal ArticleDOI
Solution of the Schrödinger equation for time-dependent 1D harmonic oscillators using the orthogonal functions invariant
TL;DR: In this paper, an extension of the classical orthogonal functions invariant to the quantum domain is presented, expressed in terms of the Hamiltonian, and unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the timedependent Schrodinger equation for a harmonic oscillator with time-dependent parameter.
Journal ArticleDOI
On the invariant method for the time-dependent non-Hermitian Hamiltonians
TL;DR: In this paper, a quasi-Hermitian transformation is proposed to deal with certain time-dependent non-hermitian Hamiltonian operators that generate a real phase in their time evolution, which implies that the dynamics is governed by unitary time evolution.
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