Schroedinger revisited:How the time-dependent wave equation follows from the Hamilton-Jacobi equation
| dc.creator | Granik, A. | |
| dc.date | 2004-09-03 | |
| dc.date | 2004-09-06 | |
| dc.date.accessioned | 2026-07-07T06:10:47Z | |
| dc.date.available | 2026-07-07T06:10:47Z | |
| dc.description | It is shown how using the classical Hamilton-Jacobi equation one can arrive at the time-dependent wave equation. Although the former equation was originally used by E.Schroedinger to get the wave equation, we propose a different approach. In the first place, we do not use the principle of least action and, in addition, we arrive at the time-dependent equation, while Schroedinger (in his first seminal paper) used the least action principle and obtained the stationary wave equation. The proposed approach works for any classical Hamilton-Jacobi equation. In addition, by introducing information loss into the Hamilton-Jacobi equation we derive in an elementary fashion the wave equations (ranging from the Shroedinger to Klein-Gordon, to Dirac equations). We also apply this technique to a relativistic particle in the gravitational field and obtain the respective wave equation. All this supports 't Hooft's proposal about a possibility of arriving at quantum description from a classical continuum in the presence of information loss. | |
| dc.description | 19 pages; Some corrections to Introduction and Conclusion | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0409018 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0409018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92347 | |
| dc.subject | Quantum Physics | |
| dc.title | Schroedinger revisited:How the time-dependent wave equation follows from the Hamilton-Jacobi equation | |
| dc.type | text |