| Issue |
EPL
Volume 89, Number 1, January 2010
|
|
|---|---|---|
| Article Number | 10003 | |
| Number of page(s) | 4 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/89/10003 | |
| Published online | 01 January 2010 | |
Proper quantization rule
1
Faculty of Science, Xi'an University of Architecture and Technology - Xi'an, 710055, China
2
Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos - Mexico D. F. 07738, Mexico
Corresponding author: dongsh2@yahoo.com
Received:
28
September
2009
Accepted:
7
December
2009
We find a proper quantization rule, 
, where n is the number of the nodes of wave function
. By this rule the energy spectra of a solvable system can be determined from its ground-state energy only. Particularly, we study three solvable quantum systems —modified Rosen-Morse potential, symmetric trigonometric Rosen-Morse potential and Manning-Rosen potential in D dimensions— with the proper quantization rule, and show that the previous complicated and tedious calculations can be greatly simplified. This proper quantization rule applies to any exactly solvable potential, and one can easily obtain its energy spectra with the rule.
This work is dedicated to Professor Zhong-Qi Ma on the occasion of his 70th birthday.
PACS: 12.39.Mk – Glueball and nonstandard multi-quark/gluon states / 12.39.Pn – Potential models / 12.40.Nn – Regge theory, duality, absorptive/optical models
© EPLA, 2010
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