Quantum Physics

    

The Sine-Gordon Breather in an Infinite Potential Well

Authors: Dennis Braun

In this paper we want to solve the motion of a breather soliton of the Sine-Gordon equation in an infinite potential well. This problem can be solved analytically for a well whose width L is far greater than the size of the soliton d, using the two breather solution of the Sine-Gordon equation. We show that this solution exhibits discrete energy levels with a quantisation condition equivalent to that obtained from quantum mechanics. They do arise in a similar way as standing waves give rise to discrete modes, with a wave and a reflected wave superimposed. The energy levels are given by the same formula as obtained from the Klein-Gordon equation of relativistic quantum mechanics for the same problem, but with a quantum constant h derived from the theory itself.

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[v1] 2024-08-06 21:02:13

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