Exact solution of inverse-square-root potential V (r) = -α/√r

被引：28
作者：
Li, Wen-Du [1 ]
Dai, Wu-Sheng [1 ,2 ,3 ]
机构：
[1] Tianjin Univ, Dept Phys, Tianjin 300072, Peoples R China
[2] Nankai Univ, LiuHui Ctr Appl Math, Tianjin 300072, Peoples R China
[3] Tianjin Univ, Tianjin 300072, Peoples R China
来源：
ANNALS OF PHYSICS | 2016年 / 373卷
关键词：
Inverse-square-root potential; Exact solution; Bound state; Scattering state; SUFFICIENT CONDITIONS; SCHRODINGER-EQUATION; BOUND-STATES; RANGE; SCATTERING; EXISTENCE;
D O I：
10.1016/j.aop.2016.07.005
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
An exact solution of the three-dimensional spherical symmetry inverse-square-root potential V (r) = alpha/root r, including scattering and bound-state solutions, is presented. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：207 / 215
页数：9
相关论文
共 24 条
[1]  
[Anonymous], EURASIP J ADV SIGNAL, DOI DOI 10.1111/j.1600-0765.2011.01407.x
[2]  
[Anonymous], 2010, J. High Energy Phys, DOI DOI 10.1007/JHEP03(2010)001
[3]  
[Anonymous], 1995, Heun's Differential Equations
[4]  
Ballentine LE., 2014, Quantum Mechanics: A Modern Development
[5]   Renormalization group approach to two-body scattering in the presence of long-range forces [J].
Barford, T ;
Birse, MC .
PHYSICAL REVIEW C, 2003, 67 (06) :640061-6400610
[6]   ON THE NUMBER OF BOUND STATES IN A CENTRAL FIELD OF FORCE [J].
BARGMANN, V .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1952, 38 (11) :961-966
[7]   Necessary and sufficient conditions for existence of bound states in a central potential [J].
Brau, F .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (38) :9907-9913
[8]   Sufficient conditions for the existence of bound states in a central potential [J].
Brau, F .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (26) :6687-6692
[9]  
Calogero F., 1965, Comm. Math. Phys., V1, P80
[10]   The number of eigenstates: counting function and heat kernel [J].
Dai, Wu-Sheng ;
Xie, Mi .
JOURNAL OF HIGH ENERGY PHYSICS, 2009, (02)
123