# Invariance of Witten's quantum mechanics under point canonical transformations

## TL;DR

This paper demonstrates that Witten's supersymmetric quantum mechanics maintains its algebraic structure under point canonical transformations and introduces new exactly solvable partner Hamiltonians that are not necessarily isospectral to the original.

## Contribution

It shows the invariance of supersymmetric algebra under point canonical transformations and constructs new non-isospectral exactly solvable partner Hamiltonians.

## Key findings

- Supersymmetric algebra remains invariant under point canonical transformations.
- Witten's quantum mechanics can be non-isospectral to the seed Hamiltonian.
- New class of exactly solvable partner Hamiltonians is generated.

## Abstract

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.