Search results for "Jacobi θ3-function"

Breakdown of separability due to confinement

2017

A simple system of two particles in a bidimensional configurational space S is studied. The possibility of breaking in S the time-independent Schrodinger equation of the system into two separated one-dimensional one-body Schrodinger equations is assumed. In this paper, we focus on how the latter property is countered by imposing such boundary conditions as confinement to a limited region of S and/or restrictions on the joint coordinate probability density stemming from the sign-invariance condition of the relative coordinate (an impenetrability condition). Our investigation demonstrates the reducibility of the problem under scrutiny into that of a single particle living in a limited domain …