2005•Chinese PhysicsOpen access

Generalized path-integral solution and coherent states of the harmonic oscillator in D -dimensions

Ma Yuquan, Jin Zhang, Chen Yong-Kang, Dai Hong

Abstract

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.

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Key concepts: Coherent states, Harmonic oscillator, Propagator, Creation and annihilation operators, Path integral formulation, Physics, Eigenvalues and eigenvectors, Operator (biology)