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Quantum Coupled Nonlinear Schrödinger System with Different Masses

Shigeki Matsutani
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Abstract

In this letter, I have considered one-dimensional quantum system with different masses $m$ and $M$, which does not appear integrable in general. However I have found an exact two-body wave function and due to the extension of the integrable system to more general system, it was concluded that the rapidity or quasi-momentum in the integrable system should be regarded as a modification of velocity rather than that of momentum. I have also considered the three-body wave function and argued its integrable condition.

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Shigeki Matsutani. 1997-07-09. Quantum Coupled Nonlinear Schrödinger System with Different Masses. https://arxiv.org/abs/solv-int/9707006

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