• Corpus ID: 189762415

Invariance of Witten's quantum mechanics under point canonical transformations

  title={Invariance of Witten's quantum mechanics under point canonical transformations},
  author={Gabriela I. Gonz{\'a}lez},
  journal={arXiv: Mathematical Physics},
  • G. González
  • Published 12 June 2019
  • Physics
  • arXiv: Mathematical Physics
We show that the supersymmetric algebra of Witten's quantum mechanics is invariant under a given point canonical transformation. It is shown that Witten's supersymmetric quantum mechanics can be isospectral or not to the seed Hamiltonian depending on the space coordinate you work on. We illustrate our results by generating a new class of exactly solvable supersymmetric partner Hamiltonians which are not isospectral to the seed Hamiltonian. 

Figures from this paper


SUSUSY quantum mechanics
The exactly solvable eigenproblems in Schr\"odinger quantum mechanics typically involve the differential"shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to
In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most
Confluent hypergeometric equations and related solvable potentials in quantum mechanics
The connection between the Schrodinger and confluent hypergeometric equations is discussed. It is shown that the factorization of the confluent hypergeometric equation gives a unifying powerful
Supersymmetry, factorisation of the Schrodinger equation and a Hamiltonian hierarchy
The author presents a systematic procedure for constructing a hierarchy of non-relativistic Hamiltonians with the property that the adjacent members of the hierarchy are 'supersymmetric partners'
Dynamical Breaking of Supersymmetry
We should be taking advantage of recent gains in our nonperturbative understanding of supersymmetric gauge theories to find the “standard” model of of dynamical supersymmetry breaking, and possibly
Solutions of the nonrelativistic wave equation with position-dependent effective mass
Given a spatially dependent mass distribution, we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wave functions are
Mapping of shape invariant potentials under point canonical transformations
The authors give explicit point canonical transformations which map twelve types of shape invariant potentials (which are known to be exactly solvable) into two potential classes. The eigenfunctions
On a New Treatment of Some Eigenvalue Problems
A new method for treating the most important eigenvalue problems in quantum mechanics is developed. The solutions can be found immediately once the equations are factorized by means of linear