Bound state of particle in delta-potential in tomographic representation of quantum mechanics

TL;DR

This paper investigates the bound states of a quantum particle in a delta potential using tomographic representation, deriving expressions for bound state tomograms and ionisation probabilities following potential changes.

Contribution

It introduces a novel application of tomographic quantum mechanics to analyze delta potential bound states and ionisation probabilities.

Findings

Bound state tomogram expressed via error function

Ionisation probability calculated from state tomograms

Ionisation probability also derived from Wigner function

Abstract

The problem of quantum particle moving in Dirac delta potential with instant changing well depth is studied by using formalism of tomographic representation of quantum mechanics.The bound state tomogram is given in terms of error function.The ionisation probability due to instant change of the potential parameter is calculated in terms of integral containing the state tomograms.The probability of ionisation is also expressed in terms of the Wigner function.