Interpolation of SUSY quantum mechanics

Abstract

Interpolation of two adjacent Hamiltonians in SUSY quantum mechanics $H_s=(1-s)A^{†}A+sA{A}^{†}$, $0\le s\le 1$ is discussed together with related operators. For a wide variety of shape-invariant degree one quantum mechanics and their `discrete' counterparts, the interpolation Hamiltonian is also shape-invariant, that is it takes the same form as the original Hamiltonian with shifted coupling constant(s).

Comments: 18 pages