# Higher Order Supersymmetric Truncated Oscillators

## TL;DR

This paper explores the supersymmetric extension of the truncated harmonic oscillator, revealing a novel rule for adding energy levels based on the transformation order, differing from traditional non-singular potentials.

## Contribution

It introduces a new criterion for adding energy levels in supersymmetric truncated oscillators, based on the integer part of half the transformation order.

## Key findings

- Maximum number of added levels is half the transformation order.
- New rule differs from the usual for non-singular potentials.
- Provides conditions for spectrum modification in supersymmetric systems.

## Abstract

We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that instead of the usual rule for non-singular potentials, where the order of the transformation corresponds to the maximum number of levels which can be added, now it is the integer part of half the order of the transformation which gives the maximum number of levels to be created.