Minimal Length Uncertainty Relations and New Shape Invariant Models

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.

11 pages, no figures

References in corpus (5)

• Supersymmetry and Quantum Mechanics
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Nonpointlike Particles in Harmonic Oscillators
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• A BPS Interpretation of Shape Invariance

Cited by in corpus (5)

• Exact solution of the Klein Gordon equation in the presence of a minimal length
• Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty
• Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations
• Spectral and thermodynamic properties of supersymmetric quantum systems with self-adjoint deformed momentum
• Potential Algebra Approach to Quantum Mechanics with Generalized Uncertainty Principle