Path Integral Discussion for Smorodinsky‐Winternitz Potentials: II. The Two‐ and Three‐Dimensional Sphere

Fortschritte der Physik/Progress of Physics

Volumn 43, Issue 6, 1995, Pages 523-563

  Grosche, C ^a   Pogosyan, G S ^b   Sissakian, A N ^b  

^a UNIVERSITY OF HAMBURG   (Germany)

^b JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84990719402     PISSN: 00158208     EISSN: 15213978     Source Type: Journal    
DOI: 10.1002/prop.2190430603     Document Type: Article

References (113)

1. The SU (1, 1) Propagator as a Path Integral Over Noncompact Groups
2. Path Integration Over Compact and Noncompact Rotation Groups
3. Group Theoretical Approach to Path Integrations on Spheres
4. Quantum‐Algebraic Description of Quantum Superintegrable Systems in Two Dimensions
5. Path Integral Treatment of the Hydrogen Atom in a Curved Space of Constant Curvature
6. Path Integral Treatment of the Hydrogen Atom in a Curved Space of Constant Curvature II
7. Path Integral Quantization of Certain Noncentral Systems with Dynamical Symmetries
8. Green Function for an Axially Symmetric Potential Field: A Path Integral Evaluation in Polar Coordinates
9. Exact Path Integral Treatment of Two Classes of Axially Symmetric Poten tials
10. Path Integral Treatment of the Harmann Potential
11. New Aspects of the Path Integrational Treatment of the Coulomb Potential
12. Exact Path Integral Solution of the Coulomb Plus Aharonov‐Bohm Potential
13. Coulomb Green's Function, in a n‐Dimensional Euclidean Space
14. Traitement Exact des Système Coulombiens, dans le Formalisme des Intégrales de Feynman, en Coordonnées Parabolique
15. Dynamical Theory in Curved Spaces. I. A. Review of the Classical Quantum Action Principles
16. Path Integrals Over SU (2) Manifold and Related Potentials
17. Solution of the Path Integral for the H‐Atom
18. Quantum Mechanics of H‐Atoms From Path Integrals
19. Superintegrability in Classical Mechanics
20. Group Theory of the Smorodinsky‐Winternitz System
21. Super‐Integrability of the Winternitz‐System
22. Space‐Time Approach to Non‐Relativistic Quantum Mechanics
23. Changing Dimension and Time: Two Well‐Founded and Practical Techniques for Path Integration in Quantum Physics
24. Application of Legendre Processes
25. Path Integration in Quantum Physics by Changing Drift and Time of the Underlying Diffusion Process
26. On Higher Symmetries in Quantum Mechanics
27. Symmetry Groups in Classical and Quantum Mechanics
28. Point Canonical Transformations in the Path Integral
29. Quadratic Algebras and Dynamics in Curved Spaces. I. Oscillator
30. Quadratic Algebras and Dynamics in Curved Spaces. II. The Kepler Problem
31. The Product Form for Path Integrals on Curved Manifolds
32. Path INtegral Solution of a Class of Potentials Related to the Pöschl‐Teller Potential
33. The Path Integral for the Kepler Problem on the Pseudosphere
34. Separation of Variables in Path Integrals and Path Integral Solution of Two Potentials on the Poincaré Upper Half‐Plane
35. Coulomb Potentials by Path‐Integration
36. Path Integral Solution of Scarf‐Like Potentials
37. Path Integral Solution of Two Potentials Related to the SO(2, 1) Dynamical Algebra
38. Path Integral Solution of a Class of Explicitly Time‐Dependent Potentials
39. On the Path Integral in Imaginary Lobachevsky Space
40. Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions, DESY preprint
41. Path Integral Discussion for Smorodinsky‐Winternitz Potentials, I. Two‐ and Three‐Dimensional Euclidean Space
42. Path Integrals on Curved Manifolds
43. Classification of Exactly Solvable Feynman Path Integrals
44. Bewegung eines Körpers in einem ringförmigen Potentialfeld
45. Construction of New Integrable Hamiltonians in Two Degrees of Freedom
46. Dynamical Symmetries in a Spherical Geometry
47. On a New Treatment of Some Eigenvalue Problems
48. A Note on the Kepler Problem in a Space of Constant Negative Curvature
49. Alternative Exact‐Path‐Integral‐Treatment of the Hydrogen Atom
50. Factorization‐Algebraization‐Path Integration and Dynamical Groups
51. Remarks on the Local Time Rescaling in Path Integration
52. The Group O(4), Separation of Variables and the Hydrogen Atom
53. A Note on a Quantum‐Mechanical Harmonic Oscillator in a Space of Constant Curvature
54. Classical and Quantum Study of a Generalized Kepler‐Coulomb System
55. On a Generalized Kepler‐Coulomb System: Interbasis Expansions
56. How to do the Time Sliced Path Integral for the H Atom
57. Summing the Spectral Representations of Pöschl‐Teller and Rosen‐Morse Fixed‐Energy Amplitudes
58. Zur Quantelung des asymmetrischen Kreisels (I–III)
59. Zur Quantelung des asymmetrischen Kreisels (I–III)
60. Zur Quantelung des asymmetrischen Kreisels (I–III)
61. Analogue of the Runge‐Lenz Vector and Energy Spectrum in the Kepler Problem on the Three‐Dimensional Sphere
62. Perturbation Theory of Kepler Motion Basedon Spinor Regularization
63. Dynamical Symmetries in a Spherical Geometry
64. On Complete Set of the Quantum Mechanical Observables on a Two‐Dimensional Sphere
65. Wave Functions for the Asymmetric Top
66. Path Integrals in Curved Spaces
67. A Systematic Search for Nonrelativistic Systems with Dynamical Symmetries
68. A Potential Function for the Vibrations of Diatomic Molecules
69. Canonical Functional Integrals in General Coordinates
70. Hamiltonian Orderings and Functional Integrals
71. The Canonical Quantization of Chiral Dynamics
72. The Weyl Correspondence and Path Integrals
73. Beugungserscheinungen an Körpern von ellipsoidischer Gestalt
74. 2u + λ u = 0 Allows the Complete Separation of Variables
75. The Canonical Formalism and Path Integrals in Curved Spaces
76. The Weyl Ordering and Path Integrals in Curved Spaces
77. Point Canonical Transformations and the Path Integrals
78. General New‐Time Formalism in the Path Integral
79. A New Exact Path Integral Treatment of the Coulomb and the Morse Potential Problems
80. A New Basis for the Representations of the Rotation Group. Lamé and Heun Polynomials
81. On the Generalization of the Duru‐Kleinert‐Propagator Transformations
82. Interbasis Sphere‐Cylinder Expansions for the Oscillator in the Three‐Dimensional Space of Constant Positive Curvature
83. Bemerkungen zur Quantenmechanik des anharmonischen Oszillators
84. The Equation for Quasiradial Functions in the Momentum Representation on a Three‐Dimensional Sphere
85. A Method of Determining Quantum Mechanical Eigenvalues and Eigenfunctions
86. Further Studies on Solving Eigenvalue Problems by Factorization
87. The Factorization of the Hypergeometric Equation
88. On Complete Sets of Observables
89. Space‐Time Transformations in Radial Path Integrals
90. Exact Path Integral Treatment of the Hydrogen Atom
91. Path Integrals in Polar Coordinates From eV to GeV
92. Note on the “Kepler Problem” in a Spherical Space, and the Factorization Method of Solving Eigenvalue Problems
93. Path Reparametrization in a Path Integral on a Finite‐Dimensional Manifold
94. Rheonomic Homogeneous Point Transformation and Reparametrization in the Path Integral
95. Remarks on Quantization of the Hydrogen Atom by the Path‐Integral Method
96. A Hydrogen Atom in the Curved Space. Expansion over Free Solutions on the Three‐Dimensional Sphere
97. Quantum Mechanics of the Little Group of the Poincaré Group
98. Time Substitution in Stochastic Processes as a Tool in Path Integration