In the past ten years, the ideas of supersymmetry have been profitably applied to many
nonrelativistic quantum mechanical problems. In particular, there is now a much deeper …

We propose a higher-order derivative generation of supersymmetric quantum mechanics. It
is formally based on the standard superalgebra but supercharges involve differential …

Known shape-invariant potentials for the constant-mass Schrödinger equation are taken as
effective potentials in a position-dependent effective mass (PDEM) one. The corresponding …

We review solvable models within the framework of supersymmetric quantum mechanics
(SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum …

In the context of some deformed canonical commutation relations leading to isotropic
nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved …

A variety of coherent states of the harmonic oscillator is considered. It is formed by a
particular superposition of canonical coherent states. In the simplest case, these …

We discuss in some detail the self-similar potentials of Shabat [Inverse Prob. 8, 303 (1992)]
and Spiridonov [Phys. Rev. Lett. 69, 298 (1992)] which are reflectionless and have an infinite …

Quantum mechanical potentials satisfying the property of shape invariance are well known
to be algebraically solvable. Using a scaling ansatz for the change of parameters, the …

An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics
is discussed. By introducing an operator which reparametrizes wave functions, the shape …

An elementary finite difference algorithm shortens the Darboux method, permitting an easy
generation of families of anharmonic potentials almost isospectral to the harmonic oscillator …