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arXiv · 1912.00657

Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect

Kenichi Aouda·Naohiro Kanda·Shigefumi Naka·Haruki Toyoda
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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.

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Kenichi Aouda, Naohiro Kanda, Shigefumi Naka, Haruki Toyoda. 2019-12-02. Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect. https://doi.org/10.1103/physrevd.102.025002

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