Hamilton-Jacobi theory and quantum mechanics. I. The free particle case

H. Rose

A. Pareek

O. Chavoya-Aceves

The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can be considered as describing the motion of an ensemble of particles that move under the action of the electromagnetic field alone, without quantum potentials, hidden uninterpreted variables, or zero point fields. The number of particles is not locally conserved.

Antonio S. de Castro, ALVARO DE SOUZA DUTRA

Teguh Budi Prayitno

We review the derivation as well as the free particle solution of nonlinear master Schrödinger equation. Even though this equation is founded by the Hamilton-Jacobi and continuity equations, the plane-wave solution does still exist for the free particle case. In addition, we will also formulate the gauge invariance form, which describes the electromagnetic interaction. In this case, the Hamilton-Jacobi equation should be modified while the continuity equation remains unchanged.

Ashok Kumar Kapoor, Prasanta Kumar Panigrahi, S. Sree Ranjani