The static electric polarizability of a particle bound by a finite potential well

TL;DR

This paper derives a formula for the static electric polarizability of a particle in a finite potential well using the Dalgarno-Lewis method, avoiding explicit continuum state calculations.

Contribution

It introduces a novel application of the Dalgarno-Lewis technique to compute polarizability without continuum states.

Findings

Derived an explicit expression for polarizability

Simplified calculation method avoiding continuum states

Potential for application to similar quantum systems

Abstract

In this paper we derive an expression for the static electric polarizability of a particle bound by a finite potential well without the explicit use of the continuum states in our calculations. This will be accomplished by employing the elegant Dalgarno-Lewis perturbative technique.