Exact wave functions and coherent states for a forced damped harmonic oscillator

Qian Shang-Wu, Gu Zhi-Yu, Wei Wang

H. G. Oh, H. R. Lee, Thomas F. George +1 more

For a damped harmonic oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) path integral, (ii) second quantization, and (iii) dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, overcomplete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.

Subir Kumar Bose, U. B. Dubey, V. N. Tewari

Hermann Grabert, Ulrich Weiß, Peter Talkner A

M. Sebawe Abdalla

An exact solution is presented for the problem of a harmonic oscillator of time-dependent mass with an external driving force. The wave functions for both pseudostationary and quasicoherent states and the Green's function are calculated. A solution is obtained in the Heisenberg picture. The amplitude for transition from a coherent state to a simple harmonic-oscillator coherent state is calculated.

Nathan A. Lanfear, Raquel M. López, Sergeĭ K. Suslov