Ladder operators and coherent states for the trigonometric P\"oschl-Teller potential

TL;DR

This paper constructs and compares coherent states for the trigonometric P"oschl-Teller potential using deformed operators and traditional ladder operators, showing both methods produce identical algebraic structures.

Contribution

It introduces a generalized approach to construct coherent states for nonlinear systems using deformed operators and confirms their equivalence with traditional methods.

Findings

Both methods produce coherent states with identical algebraic structures.

Deformed operators effectively generalize the construction of coherent states.

The approach applies to the trigonometric P"oschl-Teller potential.

Abstract

In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schr\"odinger equation. We show that both methods yield coherent states with identical algebraic structure.