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  • Elsevier  (378,659)
  • American Institute of Physics (AIP)  (49,884)
  • 1995-1999  (428,543)
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  • 1
    Electronic Resource
    Electronic Resource
    Partially solvable quantum many-body problems in D-dimensional space (D=1,2,3,...) (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4208-4226 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple technique employed almost three decades ago to manufacture partially solvable quantum many-body problems is revisited. [A quantum problem is "partially solvable" if (only) some of its eigenvalues and eigenfunctions can be exhibited]. The models thereby generated are characterized by Hamiltonians of normal form, i.e., standard kinetic plus momentum-independent potential energy; in most cases the latter features three-body, in addition to two-body and one-body, interactions. The setting refers to D-dimensional space; the examples focus on D=1, D=2, and D≥2, and include generalizations of, and additional results on, cases recently discussed in the literature, as well as new models. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532961
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  • 2
    Electronic Resource
    Electronic Resource
    Dynamical semigroups for interacting quantum and classical systems (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1300-1316 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A mathematical framework for the completely positive semigroup coupling between classical and quantum systems is proposed. The coupling ensures a flow of information from the quantum system to the classical one and the influence of the classics on the dynamics of the quantum system in a dissipative way. The classical evolution on average is modified by the expectation value of some quantum operator. Examples of a classical particle moving along a geodesic line in a curved space interacting with the quantum system, and the coupling of a two state quantum system to all pure states, are discussed. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532803
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  • 3
    Electronic Resource
    Electronic Resource
    On the anisotropic Manev problem (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1359-1375 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the Manev potential, given by the sum between the inverse and the inverse square of the distance, in an anisotropic space, i.e., such that the force acts differently in each direction. Using McGehee coordinates, we blow up the collision singularity, paste a collision manifold to the phase space, study the flow on and near the collision manifold, and find a positive-measure set of collision orbits. Besides frontal homothetic, frontal nonhomothetic, and spiraling collisions and ejections, we put into the evidence the surprising class of oscillatory collision and ejection orbits. Using the infinity manifold, we further tackle capture and escape solutions in the zero-energy case. By finding the connection orbits between equilibria and/or cycles at impact and at infinity, we describe a large class of capture-collision and ejection-escape solutions. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532807
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  • 4
    Electronic Resource
    Electronic Resource
    Rectangular well as perturbation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1163-1179 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss a finite rectangular well of a depth λ2 as a perturbation for the infinite one with λ as a perturbation parameter. In particular, we consider a behavior of energy levels in the well as functions of complex λ. It is found that all the levels of the same parity are defined on infinitely sheeted Riemann surfaces whose topological structures are described in detail. These structures differ considerably from those found in models investigated earlier. It is shown that perturbation series for all the levels converge what is in a contrast with the known results of Bender and Wu. The last property is shown to hold also for the infinite rectangular well with the Dirac delta barrier as a perturbation considered earlier by Ushveridze. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532794
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  • 5
    Electronic Resource
    Electronic Resource
    Metric symmetries and spin asymmetries of Ricci-flat Riemannian manifolds (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1255-1267 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Calabi–Yau and Joyce manifolds used in string and M-theory compactifications have no continuous groups of isometries, but they often have nontrivial discrete (actually finite) isometry groups. Discrete isometries of nonsimply connected Riemannian manifolds do not necessarily map spin structures into themselves, however; thus, inconsistencies are possible if a spin connection is used to construct the gauge vacuum. We consider this problem in detail and show how it may be avoided. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532799
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  • 6
    Electronic Resource
    Electronic Resource
    Exactly solvable models of δ′-sphere interactions in nonrelativistic quantum mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4255-4273 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We introduce and perform a systematic study of a new exactly solvable model of sphere interactions in quantum mechanics : the δ′ interaction, formally given by −Δ+αδ′(|x|−R), x∈R3, R〉0, α∈R. We also consider the cases of a δ′ plus a Coulomb interaction and finitely many δ′-sphere interactions with support on concentric spheres. For all these models, we provide basic properties and discuss the stationary scattering theory. We also briefly discuss the δ′-sphere interaction of the second type. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532964
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  • 7
    Electronic Resource
    Electronic Resource
    On a purported local extension of the quantum formalism (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4290-4295 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is widely believed that Bell has proved there can be no consistent local extension of the quantum formalism. Against this, Angelidis has presented a hidden variable theory which, he claims, makes precisely the same predictions as the quantum formalism and which also satisfies locality. In this note, we argue that Angelidis' theory does not live up to its inventor's claims. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532966
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  • 8
    Electronic Resource
    Electronic Resource
    Degeneracy and para-supersymmetry of Dirac Hamiltonian in (2+1)-space–time (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4274-4289 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum mechanics of a spin 〈fraction SHAPE="CASE"〉12 particle on a locally spatial constant curvature part of a (2+1)-space–time in the presence of a constant magnetic field of a magnetic monopole has been investigated. It has been shown that these two-dimensional Hamiltonians have the degeneracy group of SL(2,c), and para-supersymmetry of arbitrary order or shape invariance. Using this symmetry we have obtained its spectrum algebraically. The Dirac's quantization condition has been obtained from the representation theory. Also, it is shown that the presence of angular deficit suppresses both the degeneracy and shape invariance. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532965
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  • 9
    Electronic Resource
    Electronic Resource
    On one generalization for the projection matrices method in the S-matrix factorization problem (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4296-4302 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A boundary value problem for a 2×2 S-matrix is solved by the method of projection matrices. The S-matrix is assumed to be diagnoalized by orthogonal matrix U(k2)=Ω(k2)/det Ω(k2), where matrix elements of Ω(k2) are polynomials. The equation det Ω(k2)=0 has roots of any order. The example is considered for the roots with order 2. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532967
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  • 10
    Electronic Resource
    Electronic Resource
    Classical mechanics and geometric quantization on an infinite dimensional disc and Grassmannian (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4303-4324 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss the classical mechanics on the Grassmannian and the disc modeled on the ideal L(2,∞). We apply methods of geometric quantization to these systems. Their relation to a flat symplectic space is also discussed. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532968
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