5 research outputs found
N-fold Supersymmetry in Quantum Systems with Position-dependent Mass
We formulate the framework of N-fold supersymmetry in one-body quantum
mechanical systems with position-dependent mass (PDM). We show that some of the
significant properties in the constant-mass case such as the equivalence to
weak quasi-solvability also hold in the PDM case. We develop a systematic
algorithm for constructing an N-fold supersymmetric PDM system. We apply it to
obtain type A N-fold supersymmetry in the case of PDM, which is characterized
by the so-called type A monomial space. The complete classification and general
form of effective potentials for type A N-fold supersymmetry in the PDM case
are given.Comment: 18 pages, no figures; Refs. updated, typos correcte
Potential algebra approach to position dependent mass Schroedinger equation
It is shown that for a class of position dependent mass Schroedinger equation
the shape invariance condition is equivalent to a potential symmetry algebra.
Explicit realization of such algebras have been obtained for some shape
invariant potentials
Coherent state of a nonlinear oscillator and its revival dynamics
The coherent state of a nonlinear oscillator having a nonlinear spectrum is
constructed using Gazeau Klauder formalism. The weighting distribution and the
Mandel parameter are studied. Details of the revival structure arising from
different time scales underlying the quadratic energy spectrum are investigated
by the phase analysis of the autocorrelation function
A generalized quantum nonlinear oscillator
We examine various generalizations, e.g. exactly solvable, quasi-exactly
solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all
these cases, the same mass function has been used and it has also been shown
that the new exactly solvable potentials possess shape invariance symmetry. The
solutions are obtained in terms of classical orthogonal polynomials