Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length
Joint Authors
Tao, Jun
Wang, Peng
Yang, Haitang
Source
Advances in High Energy Physics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-09-16
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field.
We find the integral representation for the physically acceptable wave function in the position representation.
Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments.
We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point.
By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to O β 2 .
We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point.
The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method.
We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.
American Psychological Association (APA)
Tao, Jun& Wang, Peng& Yang, Haitang. 2015. Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length. Advances in High Energy Physics،Vol. 2015, no. 2015, pp.1-15.
https://search.emarefa.net/detail/BIM-1052570
Modern Language Association (MLA)
Tao, Jun…[et al.]. Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length. Advances in High Energy Physics No. 2015 (2015), pp.1-15.
https://search.emarefa.net/detail/BIM-1052570
American Medical Association (AMA)
Tao, Jun& Wang, Peng& Yang, Haitang. Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length. Advances in High Energy Physics. 2015. Vol. 2015, no. 2015, pp.1-15.
https://search.emarefa.net/detail/BIM-1052570
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052570