Wave function in the invariant representation and squeezed-state function of the time-dependent harmonic oscillator
Kyu Hwang Yeon, Hyon Ju Kim, Chung‐In Um, Thomas F. George, Lakshmi N. Pandey · Physical Review A · 1994
The two quantum invariant operators are found from the time-dependent Hamiltonian of the harmonic oscillator with an auxiliary condition. The solution of the Schr\"odinger equation for the system, such as the eigenfunctions, eigenvalues, and minimum uncertainty, is derived by utilizing these invariant operators. The coherent states of this system are not the squeezed states, and the eigenfunction of the invariant operator is not the eigenfunction of the Hamiltonian of the system unless it is in the invariant representation. The squeezing function, which is an eigenfunction of the Hamiltonian of the system in the invariant representation and which also gives the minimum uncertainty, is obtained by a set of unitary transformed operators, i.e., squeezing operators.