Proof to count bound state nodes in supersymmetric quantum mechanics

TL;DR

This paper establishes a method to determine the number of internal nodes in bound states of one-dimensional supersymmetric quantum mechanics using super-generator transformations and Wronskian techniques.

Contribution

It introduces a novel approach combining super-generator transformations with Wronskian methods to relate bound state nodes to excitation levels.

Findings

Ground state has zero internal nodes.

Number of nodes in excited states equals excitation level.

Method provides an elegant way to analyze bound state nodes.

Abstract

A normalizable static supersymmetric bound ground state annihilated by the super-generators has got zero number of internal nodes in the framework of one-dimensional supersymmetric quantum mechanics. The super-generator transformations between excited super-partner bound states as combined with the standard technique of Wronskian provides an elegant and self-sufficient way to derive the equality of internal nodes amount to the number of consequent excitation.