High-order Supersymmetric Quantum Mechanics

David J. Fernández C.

We review the higher‐order supersymmetric quantum mechanics (H‐SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first‐order SUSY transformations are used to derive in a simple way the higher‐order case. The second order technique is addressed directly, and through this approach unexpected possibilities for designing spectra are uncovered. The formalism is applied to the harmonic oscillator: the corresponding H‐SUSY partner Hamiltonians are ruled by polynomial Heisenberg algebras which allow a straight construction of the coherent states.

Georg Junker

M O'Connor

The author gives an explicit relation between the path integral and the operator ordering of the Hamiltonian for supersymmetric quantum mechanics. Using a stochastic differential equation the author is able to resolve the ambiguities associated with defining the supersymmetric path integral.

Asim Gangopadhyaya, Jeffry V. Mallow A, Constantin Rasinariu

Mohammed Daoud A, M. Kibler

It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k -1 copies of ordinary supersymmetric quantum mechanics.