Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect
High Energy Physics - Theory
2020-10-27 v3 Quantum Physics
Abstract
The ladder operators in harmonic oscillator are a well-known strong tool for various problems in physics. In the same sense, it is sometimes expected to handle the problems of repulsive harmonic oscillator in a similar way to the ladder operators in harmonic oscillators, though their analytic solutions are well known. In this paper, we discuss a simple algebraic way to introduce the ladder operators of the repulsive harmonic oscillators, which can reproduce well-known analytic solutions. Applying this formalism, we discuss the charged particles in a constant electric field in relation to the Schwinger effect; the discussion is also made on a supersymmetric extension of this formalism.
Keywords
Cite
@article{arxiv.1912.00657,
title = {Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect},
author = {Kenichi Aouda and Naohiro Kanda and Shigefumi Naka and Haruki Toyoda},
journal= {arXiv preprint arXiv:1912.00657},
year = {2020}
}
Comments
18pages, 3figures