Wronskian/Casoratian Identities and their Application to Quantum Mechanical Systems

Abstract

Corresponding to a certain Wronskian identity, we present two types of new Casoratian identities. We apply these identities to the Darboux transformations of quantum mechanical systems. The Wronskian identity is applied to the ordinary quantum mechanics, and the two Casoratian identities are applied to the discrete quantum mechanics with pure imaginary and real shifts, respectively.

25 pages. Comments and a reference added. To appear in J.Phys.A

References in corpus (3)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Dual Christoffel transformations
• Multi-indexed Meixner and Little $q$-Jacobi (Laguerre) Polynomials

Cited by in corpus (2)

• Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
• New Finite Type Multi-Indexed Orthogonal Polynomials Obtained From State-Adding Darboux Transformations