Self-Similar Potentials and q-Coherent States

TL;DR

This paper explores self-similar potentials through shape-invariance and derives a corresponding coherent state that reduces to a q-deformed coherent state, linking self-similarity with quantum algebra structures.

Contribution

It introduces a new formulation of self-similar potentials using shape-invariance and constructs a related coherent state that connects to q-deformed states.

Findings

Derived a coherent state for self-similar potentials.

Showed the coherent state reduces to a q-deformed state.

Linked self-similarity with q-deformed quantum states.

Abstract

The self-similar potentials are formulated in terms of the shape-invariance. Based on it, a coherent state associated with the shape-invariant potentials is calculated in case of the self-similar potentials. It is shown that it reduces to the q-deformed coherent state.