On the conection between the Liouville equation and the Schrodinger equation
| dc.creator | Carnovali Jr., Edelver | |
| dc.creator | Franca, Humberto M. | |
| dc.date | 2005-12-06 | |
| dc.date | 2006-04-17 | |
| dc.date.accessioned | 2026-07-07T06:56:33Z | |
| dc.date.available | 2026-07-07T06:56:33Z | |
| dc.description | We derive a classical Schrodinger type equation from the classical Liouville equation in phase space. The derivation is based on a Wigner type Fourier transform of the classical phase space probability distribution, which depends on an arbitrary constant $α$ with dimension of action. In order to achieve this goal two requirements are necessary: 1) It is assumed that the classical probability amplitude $Ψ(x,t)$ can be expanded in a complete set of functions $Φ_n(x)$ defined in the configuration space; 2) the classical phase space distribution $W(x,p,t)$ obeys the Liouville equation and is a real function of the position, the momentum and the time. We show that the constant $α$ appearing in the Fourier transform of the classical phase space distribution, and also in the classical Schrodinger type equation, has its origin in the spectral distribution of the vacuum zero-point radiation, and is identified with the Planck's constant $\hbar$. | |
| dc.description | Submitted to Physics Letters A. 16 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0512049 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0512049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106678 | |
| dc.subject | Quantum Physics | |
| dc.title | On the conection between the Liouville equation and the Schrodinger equation | |
| dc.type | text |