Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics

Abstract

When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.

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Cited by in corpus (8)

• The origin of the hidden supersymmetry
• Wronskian differential formula for confluent supersymmetric quantum mechanics
• Wronskian differential formula for k-confluent SUSY QM
• Extended supersymmetry of the self-isospectral crystalline and soliton chains
• Polynomial Supersymmetry for Matrix Hamiltonians
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Polynomial supersymmetry for matrix Hamiltonians: proofs