Covariance of the Schrödinger equation under low velocity boosts

Details Covariance of the Schrödinger equation under low velocity boosts Covariance of the Schrödinger equation under low velocity boosts

2004-03-02

arxiv.org/abs/quant-ph/0403013v1

Physics

Quantum Physics

5 pages, 15 equations

Scientific paper

It is known that the Schroedinger equation is not covariant under Galilei boosts, unless the phase of its solutions are shifted simultaneously. It is argued that the phase shift is not a coordinate transformation, because it depends on the mass of the Schroedinger particle. The phase shift also cannot be derived from low speed Lorentz boost. It is proposed to extend the Galilei boost with two terms of order v^2/c^2 to avoid these issues and to guarantee covariance of the Schroedinger kinetic energy and momentum. The extensions imply that proper time and relativity of simultaneity are essential features of Schroedinger quantum mechanics.

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