Kh. Yeon et al., WAVE-FUNCTION IN THE INVARIANT REPRESENTATION AND SQUEEZED-STATE FUNCTION OF THE TIME-DEPENDENT HARMONIC-OSCILLATOR, Physical review. A, 50(2), 1994, pp. 1035-1039
The two quantum invariant operators are found from the time-dependent
Hamiltonian of the harmonic oscillator with an auxiliary condition. Th
e solution of the Schrodinger equation for the system, such as the eig
enfunctions, eigenvalues, and minimum uncertainty, is derived by utili
zing these invariant operators. The coherent states of this system are
not the squeezed states, and the eigenfunction of the invariant opera
tor is not the eigenfunction of the Hamiltonian of the system unless i
t is in the invariant representation. The squeezing function, which is
an eigenfunction of the Hamiltonian of the system in the invariant re
presentation and which also gives the minimum uncertainty, is obtained
by a set of unitary transformed operators, i.e., squeezing operators.