N-fold Supersymmetry for a Periodic Potential

Details N-fold Supersymmetry for a Periodic Potential N-fold Supersymmetry for a Periodic Potential

2000-11-02

arxiv.org/abs/quant-ph/0011009v1

Phys.Lett. B498 (2001) 117-122

Physics

Quantum Physics

10 pages, 2 figures

Scientific paper

10.1016/S0370-2693(00)01355-1

We report a new type of supersymmetry, "N-fold supersymmetry", in one-dimensional quantum mechanics. Its supercharges are N-th order polynomials of momentum: It reduces to ordinary supersymmetry for N=1, but for other values of N the anticommutator of the supercharges is not the ordinary Hamiltonian, but is a polynomial of the Hamiltonian. (For this reason, the original Hamiltonian is referred to as the "Mother Hamiltonian".) This supersymmetry shares some features with the ordinary variety, the most notable of which is the non-renormalization theorem. An N-fold supersymmetry was earlier found for a quartic potential whose supersymmetry is spontaneously broken. Here we report that it also holds for a periodic potential, albeit with somewhat different supercharges, whose supersymmetry is not broken.

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