Generalized Langer correction and the exactness of WKB for all conventional potentials

被引：0
作者：
Gangopadhyaya, Asim [1 ]
Bougie, Jonathan [1 ]
Rasinariu, Constantin [1 ]
机构：
[1] Loyola Univ Chicago, Dept Phys, Chicago, IL 60660 USA
来源：
PHYSICS LETTERS A | 2023年 / 476卷
关键词：
Semiclassical approximation; WKB; Supersymmetric quantum mechanics; Shape invariance; Exactly solvable systems; SHAPE-INVARIANT POTENTIALS; SCHRODINGER-EQUATION; QUANTUM-MECHANICS; INTEGRAL APPROACH; APPROXIMATION; SUPERSYMMETRY; RESOLUTION; FORMULA; SPECTRA;
D O I：
10.1016/j.physleta.2023.128878
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quantum mechanics, we generalize the Langer correction and show that it generates the exact quantization condition for all conventional potentials. We also prove that this correction is related to the previously proven exactness of SWKB for these potentials. (c) 2023 Elsevier B.V. All rights reserved.
引用
收藏
页数：16
相关论文
共 74 条
  • [1] SEMICLASSICAL EIGENVALUES FOR POTENTIAL FUNCTIONS DEFINED ON A FINITE INTERVAL
    ADAMS, JE
    MILLER, WH
    [J]. JOURNAL OF CHEMICAL PHYSICS, 1977, 67 (12) : 5775 - 5778
  • [2] HIGHER-ORDER WKB APPROXIMATIONS IN SUPERSYMMETRIC QUANTUM-MECHANICS
    ADHIKARI, R
    DUTT, R
    KHARE, A
    SUKHATME, UP
    [J]. PHYSICAL REVIEW A, 1988, 38 (04): : 1679 - 1686
  • [3] EXACT QUANTIZATION RULES FOR 1-DIMENSIONAL SCHRODINGER EQUATION WITH TURNING POINTS
    BAILEY, PB
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1964, 5 (09) : 1293 - &
  • [4] Algebraic nature of shape-invariant and self-similar potentials
    Balantekin, AB
    Ribeiro, MAC
    Aleixo, ANF
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1999, 32 (15): : 2785 - 2790
  • [5] Algebraic approach to shape invariance
    Balantekin, AB
    [J]. PHYSICAL REVIEW A, 1998, 57 (06): : 4188 - 4191
  • [6] QUANTUM STRUCTURE OF THE MOTION GROUPS OF THE 2-DIMENSIONAL CAYLEY-KLEIN GEOMETRIES
    BALLESTEROS, A
    HERRANZ, FJ
    DELOLMO, MA
    SANTANDER, M
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (21): : 5801 - 5823
  • [7] Supersymmetric Quantum Mechanics and Solvable Models
    Bougie, Jonathan
    Gangopadhyaya, Asim
    Mallow, Jeffry
    Rasinariu, Constantin
    [J]. SYMMETRY-BASEL, 2012, 4 (03): : 452 - 473
  • [8] Generation of a Complete Set of Additive Shape-Invariant Potentials from an Euler Equation
    Bougie, Jonathan
    Gangopadhyaya, Asim
    Mallow, Jeffry V.
    [J]. PHYSICAL REVIEW LETTERS, 2010, 105 (21)
  • [9] Brillouin L, 1926, CR HEBD ACAD SCI, V183, P24
  • [10] Riccati equation, factorization method and shape invariance
    Cariñena, JF
    Ramos, A
    [J]. REVIEWS IN MATHEMATICAL PHYSICS, 2000, 12 (10) : 1279 - 1304
12345678