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| related topics |
| {energy, gaussian, time} |
| {equation, function, exp} |
| {field, particle, equation} |
| {theory, mechanics, state} |
| {phase, path, phys} |
| {time, wave, function} |
| {wave, scattering, interference} |
| {state, states, entangled} |
| {cos, sin, state} |
| {particle, mechanics, theory} |
|
On the Staruszkiewicz Modification of the Schroedinger Equation
Waldemar Puszkarz
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9912006
- categories:
- quant-ph
- comments:
- Latex, 16 pages
- arxiv_id:
- quant-ph/9912006
- created:
- 1999-12-01
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