dorsal/arxiv
View SchemaCovariance of the Schr\"odinger equation under low velocity boosts
| Authors | A B van Oosten |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403013 |
| URL | https://arxiv.org/abs/quant-ph/0403013 |
Abstract
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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"abstract": "It is known that the Schroedinger equation is not covariant under Galilei\nboosts, unless the phase of its solutions are shifted simultaneously. It is\nargued that the phase shift is not a coordinate transformation, because it\ndepends on the mass of the Schroedinger particle. The phase shift also cannot\nbe derived from low speed Lorentz boost. It is proposed to extend the Galilei\nboost with two terms of order v^2/c^2 to avoid these issues and to guarantee\ncovariance of the Schroedinger kinetic energy and momentum. The extensions\nimply that proper time and relativity of simultaneity are essential features of\nSchroedinger quantum mechanics.",
"arxiv_id": "quant-ph/0403013",
"authors": [
"A B van Oosten"
],
"categories": [
"quant-ph"
],
"title": "Covariance of the Schr\\\"odinger equation under low velocity boosts",
"url": "https://arxiv.org/abs/quant-ph/0403013"
},
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