Regularization of the singular inverse square potential in quantum mechanics with a minimal length

被引：87
作者：
Bouaziz, Djamil [1 ]
Bawin, Michel
机构：
[1] Univ Liege, Inst Phys B5, B-4000 Liege 1, Belgium
[2] Univ Jijel, Phys Theor Lab, Jijel 18000, Algeria
来源：
PHYSICAL REVIEW A | 2007年 / 76卷 / 03期
关键词：
UNCERTAINTY RELATION; HYDROGEN-ATOM; DIRAC OSCILLATOR; SPACE; RENORMALIZATION; REPRESENTATION; POSITIONS; PARTICLES; MOMENTA; STATES;
D O I：
10.1103/PhysRevA.76.032112
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically the s-wave bound states equation in terms of Heun's functions. We discuss in detail the bound states spectrum for a specific form of the generalized uncertainty relation. The minimal length may be interpreted as characterizing the dimension of the system.
引用
收藏
页数：13
相关论文
共 53 条
[1]  
Abramowitz M., 1966, HDB MATH FUNCTIONS F, P556
[2]   Minimal length uncertainty relation and the hydrogen spectrum [J].
Akhoury, R ;
Yao, YP .
PHYSICS LETTERS B, 2003, 572 (1-2) :37-42
[3]   CAN SPACETIME BE PROBED BELOW THE STRING SIZE [J].
AMATI, D ;
CIAFALONI, M ;
VENEZIANO, G .
PHYSICS LETTERS B, 1989, 216 (1-2) :41-47
[4]   Electron-bound states in the field of dipolar molecules [J].
Bawin, M .
PHYSICAL REVIEW A, 2004, 70 (02) :022505-1
[5]   Singular inverse square potential, limit cycles, and self-adjoint extensions [J].
Bawin, M ;
Coon, SA .
PHYSICAL REVIEW A, 2003, 67 (04) :5
[6]  
Bawin M, 2001, PHYS REV A, V63, DOI 10.1103/PhysRevA.63.034701
[7]   Singular potentials and limit cycles [J].
Beane, SR ;
Bedaque, PF ;
Childress, L ;
Kryjevski, A ;
McGuire, J ;
van Kolck, U .
PHYSICAL REVIEW A, 2001, 64 (04) :421031-421038
[8]   Hydrogen-atom spectrum under a minimal-length hypothesis [J].
Benczik, S ;
Chang, LN ;
Minic, D ;
Takeuchi, T .
PHYSICAL REVIEW A, 2005, 72 (01)
[9]   Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation [J].
Benczik, S ;
Chang, LN ;
Minic, D ;
Okamura, N ;
Rayyan, S ;
Takeuchi, T .
PHYSICAL REVIEW D, 2002, 66 (02) :1
[10]   Renormalization-group limit cycle for the 1/r2 potential -: art. no. 052111 [J].
Braaten, E ;
Phillips, D .
PHYSICAL REVIEW A, 2004, 70 (05) :052111-1
123456