Type B 3-fold Supersymmetry and Non-polynomial Invariant Subspaces

Abstract

We obtain the most general type B 3-fold supersymmetry by solving directly the intertwining relation. We then show that it is a necessary and sufficient condition for a second-order linear differential operator to have three linearly independent local analytic solutions. We find that there are eight linearly independent non-trivial linear differential operators of this kind. As a by-product, we find new quasi-solvable second-order operators preserving a monomial or polynomial subspace, one in type B, two in type C, and four in type X_2, all of which have been missed in the existing literature. In addition, we show that type A, type B, and type C 3-fold supersymmetries are connected continuously via one parameter. A few new quasi-solvable models are also presented.

32 pages, no figures; 2 sections and 1 appendix added, published version

References in corpus (6)

• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• A New Family of N-fold Supersymmetry: Type B
• A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry
• Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry
• Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry II. The N=3 Case
• On General Form of N-fold Supersymmetry

Cited by in corpus (1)

• GL(3,C) Invariance of Type B 3-fold Supersymmetric Systems