1,857 research outputs found
Alternative Solution of the Path Integral for the Radial Coulomb Problem
In this Letter I present an alternative solution of the path integral for the
radial Coulomb problem which is based on a two-dimensional singular version of
the Levi-Civita transformation.Comment: 7 pages, Late
Path Integral Discussion of Two and- Three-Dimensional -Function Perturbations
The incorporation of two- and three-dimensional -function
perturbations into the path-integral formalism is discussed. In contrast to the
one-dimensional case, a regularization procedure is needed due to the
divergence of the Green-function , (\vec x,\vec
y\in\bbbr^2,\bbbr^3) for , corresponding to a potential problem
. The known procedure to define proper self-adjoint extensions for
Hamiltonians with deficiency indices can be used to regularize the path
integral, giving a perturbative approach for -function perturbations in
two and three dimensions in the context of path integrals. Several examples
illustrate the formalism.Comment: 32 pages, AmSTe
On the Path Integral Treatment for an Aharonov-Bohm Field on the Hyperbolic Plane
In this paper I discuss by means of path integrals the quantum dynamics of a
charged particle on the hyperbolic plane under the influence of an
Aharonov-Bohm gauge field. The path integral can be solved in terms of an
expansion of the homotopy classes of paths. I discuss the interference pattern
of scattering by an Aharonov-Bohm gauge field in the flat space limit, yielding
a characteristic oscillating behavior in terms of the field strength. In
addition, the cases of the isotropic Higgs-oscillator and the Kepler-Coulomb
potential on the hyperbolic plane are shortly sketched.Comment: LaTeX 12 pp., one figur
Path Integrals with Kinetic Coupling Potentials
Path integral solutions with kinetic coupling potentials are
evaluated. As examples I give a Morse oscillator, i.e., a model in molecular
physics, and the double pendulum in the harmonic approximation. The former is
solved by some well-known path integral techniques, whereas the latter by an
affine transformation.Comment: 8 pages., LateX, 1 figure (postscript
Path Integral Approach for Spaces of Non-constant Curvature in Three Dimensions
In this contribution I show that it is possible to construct
three-dimensional spaces of non-constant curvature, i.e. three-dimensional
Darboux-spaces. Two-dimensional Darboux spaces have been introduced by Kalnins
et al., with a path integral approach by the present author. In comparison to
two dimensions, in three dimensions it is necessary to add a curvature term in
the Lagrangian in order that the quantum motion can be properly defined. Once
this is done, it turns out that in the two three-dimensional Darboux spaces,
which are discussed in this paper, the quantum motion is similar to the
two-dimensional case. In \threedDI we find seven coordinate systems which
separate the Schr\"odinger equation. For the second space, \threedDII, all
coordinate systems of flat three-dimensional Euclidean space which separate the
Schr\"odinger equation also separate the Schr\"odinger equation in
\threedDII. I solve the path integral on \threedDI in the -system,
and on \threedDII in the -system and in spherical coordinates
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