dorsal/arxiv
View SchemaOn the Staruszkiewicz Modification of the Schroedinger Equation
| Authors | Waldemar Puszkarz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9912006 |
| URL | https://arxiv.org/abs/quant-ph/9912006 |
Abstract
We discuss Staruszkiewicz's nonlinear modification of the Schr\"{o}dinger equation. It is pointed out that the expression for the energy functional for this modification is not unique as the field-theoretical definition of energy does not coincide with the quantum-mechanical one. As a result, this modification can be formulated in three different ways depending on which physically relevant properties one aims to preserve. Some nonstationary one-dimensional solutions for suitably chosen potentials, including a KdV soliton, are presented, and the question of finding stationary solutions is also discussed. The analysis of physical and mathematical features of the modification leads to the conclusion that the Staruszkiewicz modification is a very subtle modification of the fundamental equation of quantum mechanics.
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"abstract": "We discuss Staruszkiewicz\u0027s nonlinear modification of the Schr\\\"{o}dinger\nequation. It is pointed out that the expression for the energy functional for\nthis modification is not unique as the field-theoretical definition of energy\ndoes not coincide with the quantum-mechanical one. As a result, this\nmodification can be formulated in three different ways depending on which\nphysically relevant properties one aims to preserve. Some nonstationary\none-dimensional solutions for suitably chosen potentials, including a KdV\nsoliton, are presented, and the question of finding stationary solutions is\nalso discussed. The analysis of physical and mathematical features of the\nmodification leads to the conclusion that the Staruszkiewicz modification is a\nvery subtle modification of the fundamental equation of quantum mechanics.",
"arxiv_id": "quant-ph/9912006",
"authors": [
"Waldemar Puszkarz"
],
"categories": [
"quant-ph"
],
"title": "On the Staruszkiewicz Modification of the Schroedinger Equation",
"url": "https://arxiv.org/abs/quant-ph/9912006"
},
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