Finite oscillator obtained through finite frame quantization

TL;DR

This paper introduces a finite oscillator model derived from finite frame quantization, providing a new perspective on harmonic oscillator representation and potential applications in discrete fractional Fourier transforms.

Contribution

It presents a novel finite oscillator constructed via finite frame quantization, bridging continuous and discrete quantum models.

Findings

Finite oscillator defined through finite frame quantization.

Potential application to discrete fractional Fourier transform.

Provides a finite-dimensional analog of the harmonic oscillator.

Abstract

The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the coherent state quantization and it allows us to define a finite oscillator by starting from the integral representation of the harmonic oscillator. Our purpose is to investigate the oscillator obtained in this way, and to present a possible application to the discrete fractional Fourier transform.