s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions

Abstract

We examine the zero-range limit of the finite square well in arbitrary dimensions through a systematic analysis of the reduced, s-wave two-body time-independent Schrödinger equation. A natural consequence of our investigation is the requirement of a delta-function multiplied by a regularization operator to model the zero-range limit of the finite-square well when the dimensionality is greater than one. The case of two dimensions turns out to be surprisingly subtle, and needs to be treated separately from all other dimensions.

References in corpus (5)

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Cited by in corpus (6)

• The $s$-wave scattering length of a Gaussian potential
• Effect of electron-phonon interaction on the formation of one-dimensional electronic states in coupled Cl vacancies
• Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach
• Pseudopotential for the 2D contact interaction
• The Zel'dovich effect in harmonically trapped, ultra-cold quantum gases
• Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics