Finite oscillator obtained through finite frame quantization

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.

Several new results and figures have been added

References in corpus (3)

• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Jacobi Theta-functions and Discrete Fourier Transforms
• Properties of finite Gaussians and the discrete-continuous transition

Cited by in corpus (3)

• Theoretical formulation of finite-dimensional discrete phase spaces: II. On the uncertainty principle for Schwinger unitary operators
• On the discrete Wigner function for SU(N)
• Mixed discrete variable Gaussian states