WAVE-FUNCTION IN THE INVARIANT REPRESENTATION AND SQUEEZED-STATE FUNCTION OF THE TIME-DEPENDENT HARMONIC-OSCILLATOR

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.