|
| related topics |
| {equation, function, exp} |
| {field, particle, equation} |
| {classical, space, random} |
| {wave, scattering, interference} |
| {time, wave, function} |
| {theory, mechanics, state} |
| {phase, path, phys} |
| {cos, sin, state} |
| {particle, mechanics, theory} |
|
Quantum Mechanics from the Hamilton-Jacobi Point of View
Alexander Jurisch
abstract: In this article, we develop quantum mechanics upon the framework of the
quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger
point of view and the Hamilton-Jacobi point of view are fully equivalent in
their description of physical systems, but differ in their descriptive manner.
As a main result, a wave function in Hamilton-Jacobi theory can be decomposed
into travelling waves in any point in space, not only asymptotically. The well
known WKB-theory will be a special result of the more general theory, we will
develop below. By the example of the linear potential and the harmonic
oscillator, we will discuss quantum mechanics from the Hamilton-Jacobi point of
view. Soft boundary value problems as the connection problem can be solved
exactely. Quantizised energies and Maslov-indices can be calculated directely
without orthonormalizing wave-functions. Also, we will focus on trajectory
themes, which, in contrast to the Schroedinger point of view, follow naturally
from the quantum mechanical action function.
- oai_identifier:
- oai:arXiv.org:quant-ph/0612217
- categories:
- quant-ph
- comments:
- 19 pages, 7 figures
- arxiv_id:
- quant-ph/0612217
- created:
- 2006-12-27
Full article ▸
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