Supersymmetric quantum mechanics

A standard set of solvable potentials with critical behavior can be found in many text books on quantum mechanics [49,50], like the usual square-well potentials and other piecewise constant potentials. Also there are many potentials that are solvable only at d - 1 or for three-dimensional, v waves like the Hulthen potential, the Eckart potential, and the Posch-Teller potential. These potentials belong to a class of potentials, called shape-invariant potentials, that are exactly solvable using supersymmetric quantum mechanics [51,52], There are also many approaches to make isospectral deformation of these potentials [51,53] therefore it is possible to construct nonsymmetrical potentials with the same critical behavior as that of the original symmetric problem. 

Chou, C.-C., T. Markovich, and D. J. Kouri. 2012. Adiabatic switching approach to multidimensional supersymmetric quantum mechanics for several excited states. Molecular... 

Komi, D. 1., T. Markovich, N. Maxwell, and E. R. Bittner. 2009. Supersymmetric quantum mechanics, excited state energies and wave functions, and the Rayleigh-Ritz variational principle a proof of principle study. Journal of Physical Chemistry A 113 (52) 15257. 

Supersymmetric quantum mechanics can be described by a pair of related Hamiltonians... 

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