On the conection between the Liouville equation and the Schrodinger equation

dc.creatorCarnovali Jr., Edelver
dc.creatorFranca, Humberto M.
dc.date2005-12-06
dc.date2006-04-17
dc.date.accessioned2026-07-07T06:56:33Z
dc.date.available2026-07-07T06:56:33Z
dc.descriptionWe 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.descriptionSubmitted to Physics Letters A. 16 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0512049
dc.identifierhttp://arxiv.org/abs/quant-ph/0512049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106678
dc.subjectQuantum Physics
dc.titleOn the conection between the Liouville equation and the Schrodinger equation
dc.typetext

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