dorsal/arxiv
View Schema75 Years of the Wavefunction: Complex-Dynamical Extension of the Original Wave Realism and the Universal Schroedinger Equation
| Authors | Andrei P. Kirilyuk |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101129 |
| URL | https://arxiv.org/abs/quant-ph/0101129 |
Abstract
Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed, at the beginning of 1926, the concept of wavefunction and wave equation for it. Though endowed with a realistic undular interpretation by its father, the wavefunction could not be considered as a real "matter wave" and has been provided with only abstract, formally probabilistic interpretation. In this paper we show how the resulting "mysteries" of usual theory are solved within the unreduced, dynamically multivalued description of the underlying, essentially nonlinear interaction process (quant-ph/9902015, quant-ph/9902016), without artificial modification of the Schroedinger equation. The latter is rigorously derived instead as universal expression of unreduced interaction complexity. Causal, totally realistic wavefunction is obtained as a dynamically probabilistic intermediate state of a simple system with interaction performing dynamically discrete transitions between its localised, incompatible "realisations" ("corpuscular" states). Causal wavefunction and Schroedinger equation are then extended to arbitrary level of world dynamics. We outline some applications of the obtained causal description, such as genuine quantum chaos (quant-ph/9511034-36) and realistic quantum devices (physics/0211071), and emphasize the basic difference of the proposed dynamically multivalued theory from dynamically single-valued imitations of causality and complexity. The causally complete wavefunction concept, representing the unified essence of unreduced (multivalued) complex dynamics, provides a clear distinctive feature of realistic science, absent in any its unitary imitation.
{
"annotation_id": "5c0cfbfa-f633-4902-a66c-d7eec1164d27",
"date_created": "2026-03-02T18:01:42.307000Z",
"date_modified": "2026-03-02T18:01:42.307000Z",
"file_hash": "4f5e7e626e36684fa937a2ba67862ce4663285c6017a1faf54396c6382b1c0ae",
"private": false,
"record": {
"abstract": "Following Max Planck\u0027s hypothesis of quanta (quant-ph/0012069) and the matter\nwave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed,\nat the beginning of 1926, the concept of wavefunction and wave equation for it.\nThough endowed with a realistic undular interpretation by its father, the\nwavefunction could not be considered as a real \"matter wave\" and has been\nprovided with only abstract, formally probabilistic interpretation. In this\npaper we show how the resulting \"mysteries\" of usual theory are solved within\nthe unreduced, dynamically multivalued description of the underlying,\nessentially nonlinear interaction process (quant-ph/9902015, quant-ph/9902016),\nwithout artificial modification of the Schroedinger equation. The latter is\nrigorously derived instead as universal expression of unreduced interaction\ncomplexity. Causal, totally realistic wavefunction is obtained as a dynamically\nprobabilistic intermediate state of a simple system with interaction performing\ndynamically discrete transitions between its localised, incompatible\n\"realisations\" (\"corpuscular\" states). Causal wavefunction and Schroedinger\nequation are then extended to arbitrary level of world dynamics. We outline\nsome applications of the obtained causal description, such as genuine quantum\nchaos (quant-ph/9511034-36) and realistic quantum devices (physics/0211071),\nand emphasize the basic difference of the proposed dynamically multivalued\ntheory from dynamically single-valued imitations of causality and complexity.\nThe causally complete wavefunction concept, representing the unified essence of\nunreduced (multivalued) complex dynamics, provides a clear distinctive feature\nof realistic science, absent in any its unitary imitation.",
"arxiv_id": "quant-ph/0101129",
"authors": [
"Andrei P. Kirilyuk"
],
"categories": [
"quant-ph",
"nlin.CD",
"physics.hist-ph"
],
"title": "75 Years of the Wavefunction: Complex-Dynamical Extension of the Original Wave Realism and the Universal Schroedinger Equation",
"url": "https://arxiv.org/abs/quant-ph/0101129"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "078bfcc7-1311-47b7-af8b-210c7c47aa71",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}