| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
Relations Between Low-lying Quantum Wave Functions and Solutions of the Hamilton-Jacobi Equation | R. Friedberg
; T. D. Lee
; W. Q. Zhao
; | Date: |
12 Oct 1999 | Subject: | quant-ph | Abstract: | We discuss a new relation between the low lying Schroedinger wave function of a particle in a one-dimentional potential V and the solution of the corresponding Hamilton-Jacobi equation with -V as its potential. The function V is $geq 0$, and can have several minina (V=0). We assume the problem to be characterized by a small anhamornicity parameter $g^{-1}$ and a much smaller quantum tunneling parameter $epsilon$ between these different minima. Expanding either the wave function or its energy as a formal double power series in $g^{-1}$ and $epsilon$, we show how the coefficients of $g^{-m}epsilon^n$ in such an expansion can be expressed in terms of definite integrals, with leading order term determined by the classical solution of the Hamilton-Jacobi equation. A detailed analysis is given for the particular example of quartic potential $V={1/2}g^2(x^2-a^2)^2$. | Source: | arXiv, quant-ph/9910047 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |