Minimal Length Uncertainty Relations and New Shape Invariant Models

TL;DR

This paper introduces a new class of exactly solvable quantum models based on minimal length uncertainty relations, expanding the scope of shape invariance to include non-adjoint operator pairings.

Contribution

It presents novel shape invariant models incorporating minimal length uncertainty, demonstrating their broader applicability in quantum mechanics.

Findings

New shape invariant models based on minimal length uncertainty relations

Operators paired as non-adjoints expand shape invariance applicability

Enhanced exactly solvable quantum systems with string-motivated features

Abstract

This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our construction is the pairing of operators that are not adjoints of each other. The results in this paper thus show the broader applicability of shape invariance to exactly solvable systems.