Broken Supersymmetric Shape Invariant Systems and Their Potential Algebras

Abstract

Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is no zero energy eigenstate. We describe a novel two-step shape invariance approach as well as a group theoretic potential algebra approach for solving such broken supersymmetry problems.

Latex file, 10 pages

Cited by in corpus (12)

• Non-Hermitian supersymmetry and singular PT symmetrized oscillators
• A generalized quantum nonlinear oscillator
• Comment on "Supersymmetry and Singular Potentials" by Das and Pernice [Nucl. Phys. B 561 (1999) 357]
• Shape Invariant Potentials in Supersymmetric Quantum Cosmology
• Potential algebra approach to position dependent mass Schroedinger equation
• A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
• Exactness of Semiclassical Quantization Rule for Broken Supersymmetry
• Algebraic Shape Invariant Potentials as the Generalized Deformed Oscillator
• Two-step Shape Invariance in the Framework of N-fold Supersymmetry
• Almost-zero-energy Eigenvalues of Some Broken Supersymmetric Systems
• On the SUSY structure of spherically symmetric Pauli Hamiltonians
• Quantum Hamilton-Jacobi Quantization and Shape Invariance