Coherent States and the Propagator for the Harmonic Oscillator

G. Dattoli, A. Torre, S. Lorenzutta +1 more

Ma Yu-Quan, Jin Zhang, Chen Yong-Kang +1 more

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time-dependent forced harmonic oscillator in D ( D ⩾ 1) dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D -dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Rainer Dick

Jing‐Bo Xu, Ji-Ming Bao, Xiao-Chun Gao

The exact propagator and invariant for the time-dependent quadratic Hamiltonian is found by a generalized canonical transformation and a path integral method. We then proceed to construct the coherent states for the system by making use of the propagator. The coherent states for the damped harmonic oscillator and variable mass or frequency harmonic oscillator are the special cases of the coherent states for the system studied in this paper.

Rainer Dick