Analytic properties of energy levels in models with delta-function potentials

Abstract

The analytic properties of energy levels as the functions of coupling parameters in one-dimensional quantum mechanical models described by the potentials of delta-function type are investigated. The following models are considered: (i) the rectangular potential well with delta-function barrier, (ii) two delta-function wells in the unbounded space, (iii) the Kronig-Penney model with periodic delta-function potential, and (iv) the Bose gas with delta-function interaction between particles.