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  • 1
    Electronic Resource
    Electronic Resource
    Exact path integral solution of the Coulomb plus Aharonov–Bohm potential (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 655-658 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Green's function for the sum of the Coulomb and Aharonov–Bohm potentials is calculated exactly in the path integral formalism. The energy spectrum is deduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528433
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  • 2
    Electronic Resource
    Electronic Resource
    Path integral solution for a particle confined in a region (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 838-841 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The propagator relative to a particle constrained to move in a finite region of space is calculated in the framework of path integrals. This region of the three-dimensional space is delimited through a sector of opening angle α, and also through the action of two attractive harmonic potentials, one being central and located in the 0xy plan, and the other directed along the z axis, with respective pulsations ω and ω0. It is shown that for α=π/2 and π the propagator is the sum of propagators evaluated on classical paths. The important case of the edge (α=2π) is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528817
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  • 3
    Electronic Resource
    Electronic Resource
    The hydrogen atom in phase space (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 598-604 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Hamiltonian of the three-dimensional hydrogen atom is reduced, in parabolic coordinates, to the Hamiltonians of two bidimensional harmonic oscillators, by doing several space-time transformations,separating the movement along the three parabolic directions (ξ,η,φ), and introducing two auxiliary angular variables ψ and ψ', 0≤ψ, ψ'≤2π. The Green's function is developed into partial Green's functions, and expressed in terms of two Green's functions that describe the movements along both the ξ and η axes. Introducing auxiliary Hamiltonians allows one to calculate the Green's function in the configurational space, via the phase-space evolution function of the two-dimensional harmonic oscillator. The auxiliary variables ψ and ψ' are eliminated by projection. The thus-obtained Green's function, save for a multiplicating factor, coincides with that calculated following the path-integral formalism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527645
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Path integral treatment for a screened potential (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 441-446 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The propagator relative to an effective screened potential, which generalizes the Hulthén potential and the Kepler problem, is calculated via the path integration over the noncompact group SU(1,1). The energy spectrum and the wave functions of bound and scattering states, are deduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529431
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  • 5
    Electronic Resource
    Electronic Resource
    Algebraic treatment of a general noncentral potential (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3410-3418 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the problem of a particle moving in a noncentral potential generalizing the Coulomb potential and the Hartmann ring-shaped potential accepts SO(2,1)⊗SO(2,1) as a dynamical group, within the framework of the Kustaanheimo–Stiefel transformation. The Green's function relative to this compound potential is calculated through the algebraic approach so(2,1) and with the help of the Baker–Campbell–Hausdorff formulas. The energy spectrum and the normalized wave functions of the bound states can then be deduced. Eventually, the Coulomb potential, the Hartmann ring-shaped potential and also, due to its close link with the latter, the compound Coulomb plus Aharonov–Bohm potential may all be considered as particular cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529889
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  • 6
    Electronic Resource
    Electronic Resource
    Algebraic treatment of super-integrable potentials (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4684-4706 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The so(2,1) Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky–Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed the Green's functions for two important super-integrable potentials in R2. Among the super-integrable potentials in R3, we have considered two examples, one is maximally super-integrable and another one minimally super-integrable. The discussion is made in various coordinate systems. The energy spectrum and the suitably normalized wave functions of bound and continuous states are then deduced. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1396635
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  • 7
    Electronic Resource
    Electronic Resource
    Path integral for spinning particle in magnetic field via bosonic coherent states (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 1602-1615 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the coherent states representation and the Schwinger boson model, the propagator of a spinning particle in interaction with an arbitrary magnetic field is derived in the framework of the path integral formalism. To show the relevance of the formalism to some applications, the Green function of spinning particle s=1/2 in special configuration of magnetic field is calculated. The transition amplitude and Berry's phase for an arbitrary spin and time dependent magnetic field are deduced. The case of half integer spin is also considered. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531072
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  • 8
    Electronic Resource
    Electronic Resource
    Path integral for the damped harmonic oscillator coupled to its dual (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1185-1191 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The time independent Bateman model which describes the damped harmonic oscillator coupled to its dual is studied using the path integral approach. The related propagator is calculated by means of the matrix representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530634
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  • 9
    Electronic Resource
    Electronic Resource
    Algebraic treatment of the Kaluza–Klein monopole system (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 1016-1028 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In analogy to the Kepler problem, the Green's function for a particle in the background of the Kaluza–Klein monopole is constructed through the algebraic approach, with the help of the Kustaanheimo–Stiefel variables and the generators of the SO(2,1) group in the exponential representation of Schwinger. The bound and continuum states are also obtained. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531172
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  • 10
    Electronic Resource
    Electronic Resource
    Path integral treatment for the one-dimensional Natanzon potentials (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 1257-1269 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Green's function relative to the one-dimensional Natanzon potentials is exactly calculated by the path integral approach. The energy spectrum, the wave functions, and the scattering function S are deduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530207
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