Path Integral Discussion for Smorodinsky‐Winternitz Potentials: I. Two‐ and Three Dimensional Euclidean Space
Identifieur interne : 001D44 ( Main/Exploration ); précédent : 001D43; suivant : 001D45Path Integral Discussion for Smorodinsky‐Winternitz Potentials: I. Two‐ and Three Dimensional Euclidean Space
Auteurs : C. Grosche [Allemagne] ; G. S. Pogosyan [Russie] ; A. N. Sissakian [Russie]Source :
- Fortschritte der Physik/Progress of Physics [ 0015-8208 ] ; 1995.
English descriptors
- Teeft :
- Academic press, Cartesian, Cartesian coordinates, Chetouani, Circular elliptic, Circular elliptic coordinates, Circular parabolic, Circular parabolic coordinates, Conical, Conical coordinates, Constant curvature, Continuous spectrum, Coordinate, Corresponding path integral formulations, Cosh, Coulomb, Curved spaces, Dynamical, Dynamical group, Eigenvalue problems, Ellipsoidal, Elliptic, Elliptic coordinates, Euclidean, Euclidean space, Exact path integral treatment, Exact solution, Explicit path integration, Feynman, Feynman path integral, Flat space, Fortschr, Green function, Grosche, Group structure, Hamiltonian, Harmonic, Harmonic analysis, Harmonic oscillator, Hartmann, Homogeneous spaces, Hydrogen atom, Independent integrals, Inomata, Integral, Interbasis, Interbasis expansions, Interfocus distance, Kepler, Kepler problem, Kleinert, Lett, Math, Maximally, Maximally potentials, Mcgraw hill, Metric, Metric tensor, Momentum operators, Nuovo cimento, Oblate, Oblate spheroidal coordinates, Oscillator, Parabolic, Parabolic bases, Parabolic coordinates, Parabolic separation, Paraboloidal, Paraboloidal coordinates, Path integral, Path integral discussion, Path integral evaluations, Path integral formulation, Path integral formulations, Path integral identity, Path integral solution, Path integral solutions, Path integral treatment, Path integrals, Path integration, Phys, Pogosyan, Polar coordinates, Potential problem, Prolate, Prolate spheroidal, Propagator, Quantum chem, Quantum mechanics, Schrodinger, Schrodinger equation, Separable, Sin2v, Sinh, Sissakian, Smorodinsky, Special cases, Spectral expansion, Spectral expansions, Spherical coordinates, Spherical functions, Spheroidal, Steiner, Theor, Theoretical physics, Variable substitution, Winternitz.
Abstract
Path integral formulations for the Smorodinsky‐Winternitz potentials in two‐ and three‐dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky‐Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave‐functions.
Url:
DOI: 10.1002/prop.2190430602
Affiliations:
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We mention all coordinate systems which separate the Smorodinsky‐Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave‐functions.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Russie</li></country></list><tree><country name="Allemagne"><noRegion><name sortKey="Grosche, C" sort="Grosche, C" uniqKey="Grosche C" first="C." last="Grosche">C. Grosche</name></noRegion></country><country name="Russie"><noRegion><name sortKey="Pogosyan, G S" sort="Pogosyan, G S" uniqKey="Pogosyan G" first="G. S." last="Pogosyan">G. S. Pogosyan</name></noRegion><name sortKey="Sissakian, A N" sort="Sissakian, A N" uniqKey="Sissakian A" first="A. N." last="Sissakian">A. N. 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