dorsal/arxiv
View SchemaOn Solutions to the Nonlinear Phase Modification of the Schroedinger Equation
| Authors | Waldemar Puszkarz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9903010 |
| URL | https://arxiv.org/abs/quant-ph/9903010 |
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.
{
"annotation_id": "992343a2-2f87-4dc7-aeb6-cd5204e5c970",
"date_created": "2026-03-02T18:02:45.029000Z",
"date_modified": "2026-03-02T18:02:45.029000Z",
"file_hash": "c126a89cb0d43df6d97ed53c44fc29e39e2991736346e869a4d9f914e6d9b4da",
"private": false,
"record": {
"abstract": "We present some physically interesting, in general non-stationary,\none-dimensional solutions to the nonlinear phase modification of the\nSchr\\\"{o}dinger equation proposed recently. The solutions include a coherent\nstate, a phase-modified Gaussian wave packet in the potential of harmonic\noscillator whose strength varies in time, a free Gaussian soliton, and a\nsimilar soliton in the potential of harmonic oscillator comoving with the\nsoliton. The last of these solutions implies that there exist an energy level\nin the spectrum of harmonic oscillator which is not predicted by the linear\ntheory. The free solitonic solution can be considered a model for a particle\naspect of the wave-particle duality embodied in the quantum theory. The\nphysical size of this particle is naturally rendered equal to its Compton\nwavelength in the subrelativistic framework in which the self-energy of the\nsoliton is assumed to be equal to its rest-mass energy. The solitonic solutions\nexist only for the negative coupling constant for which the Gaussian wave\npackets must be larger than some critical finite size if their energy is to be\nbounded, i.e., they cannot be point-like objects.",
"arxiv_id": "quant-ph/9903010",
"authors": [
"Waldemar Puszkarz"
],
"categories": [
"quant-ph"
],
"title": "On Solutions to the Nonlinear Phase Modification of the Schroedinger Equation",
"url": "https://arxiv.org/abs/quant-ph/9903010"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a3d24a88-2fa8-4db7-90e0-f7f43925c320",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}