|
| related topics |
| {energy, gaussian, time} |
| {field, particle, equation} |
| {equation, function, exp} |
| {time, wave, function} |
| {particle, mechanics, theory} |
| {wave, scattering, interference} |
| {energy, state, states} |
| {phase, path, phys} |
| {cos, sin, state} |
|
On Solutions to the Nonlinear Phase Modification of the Schroedinger
Equation
Waldemar Puszkarz
abstract: We present some physically interesting, in general non-stationary,
one-dimensional solutions to the nonlinear phase modification of the
Schr\"{o}dinger equation proposed recently. The solutions include a coherent
state, a phase-modified Gaussian wave packet in the potential of harmonic
oscillator whose strength varies in time, a free Gaussian soliton, and a
similar soliton in the potential of harmonic oscillator comoving with the
soliton. The last of these solutions implies that there exist an energy level
in the spectrum of harmonic oscillator which is not predicted by the linear
theory. The free solitonic solution can be considered a model for a particle
aspect of the wave-particle duality embodied in the quantum theory. The
physical size of this particle is naturally rendered equal to its Compton
wavelength in the subrelativistic framework in which the self-energy of the
soliton is assumed to be equal to its rest-mass energy. The solitonic solutions
exist only for the negative coupling constant for which the Gaussian wave
packets must be larger than some critical finite size if their energy is to be
bounded, i.e., they cannot be point-like objects.
- oai_identifier:
- oai:arXiv.org:quant-ph/9903010
- categories:
- quant-ph
- comments:
- New organization of the paper, modified, but no changes in the
results, new references added, Latex, 13 pages
- arxiv_id:
- quant-ph/9903010
- created:
- 1999-03-03
- updated:
- 1999-05-16
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