Minimum Uncertainty States Using n-Dependent Annihilation Operator

Abstract

In the last ten years there has been tremendous interest in the study of quantum mechanical states which give minimum value to the uncertainty product [1]. Several methods [2] have been proposed to obtain such states. The simplest being the annihilation operator method, in which one first constructs the step-down operator which gives the state |n — 1) operating on the state In) of the system. The minimum uncertainty state is then obtained by solving the eigenstate of the annihilation operator. In several problems of physical interest it happens that the annihilation operator depends on n. The purpose of the present work is to develop a formalism to construct minimum uncertainty states using such annihilation operators. We shall use the three-dimensional harmonic oscillator to bring out the essential features of the present formalism, which is given in the next section. Concluding remarks are presented in Sec. 4.