Quantum harmonic oscillator with time dependent mass

Abstract

We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schrödinger equation by using squeeze operators. Finally we give two examples of time dependencies: quadratically and hyperbolically growing masses.

References in corpus (7)

• Implementation of Quantum and Classical Discrete Fractional Fourier Transforms
• Ion-laser interactions: The most complete solution
• Dynamical symmetries and the Ermakov invariant
• Dynamical Casimir effect in stochastic systems: photon-harvesting through noise
• Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator
• Electromagnetic wave propagation through inhomogeneous material layers
• Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian

Cited by in corpus (7)

• Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations
• Ermakov-Lewis invariant in Koopman-von Neumann mechanics
• Bohm potential for the time dependent harmonic oscillator
• Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians
• Temporal factorization of a non-stationary electromagnetic cavity field
• A real expectation value of the time-dependent non-Hermitian Hamiltonians
• Engineering two-mode squeezed vacuum-like states by using the Bohm potential