Extended Coherent States

TL;DR

This paper constructs and analyzes coherent states for rational extensions of the harmonic oscillator using algebraic methods, showing they are exact solutions and asymptotically minimize uncertainty.

Contribution

It introduces a novel algebraic framework for rational extensions of the harmonic oscillator and constructs coherent states with specific properties.

Findings

Coherent states are exact solutions of the time-dependent Schrödinger equation.

These states asymptotically minimize position-momentum uncertainty.

The algebraic formalism employs Maya diagrams and Schur functions.

Abstract

Using the formalism of Maya diagrams and ladder operators, we describe the algebra of annihilating operators for the class of rational extensions of the harmonic oscillator. This allows us to construct the corresponding coherent state in the sense of Barut and Girardello. The resulting time-dependent function is an exact solution of the time-dependent Schr\"odinger equation and a joint eigenfunction of the algebra of annihilators. Using an argument based on Schur functions, we also show that the newly exhibited coherent states asymptotically minimize position-momentum uncertainty.