25 research outputs found
Self-adjoint extensions and spectral analysis in the generalized Kratzer problem
We present a mathematically rigorous quantum-mechanical treatment of a
one-dimensional nonrelativistic motion of a particle in the potential field
. For and , the potential is
known as the Kratzer potential and is usually used to describe molecular energy
and structure, interactions between different molecules, and interactions
between non-bonded atoms. We construct all self-adjoint Schrodinger operators
with the potential and represent rigorous solutions of the corresponding
spectral problems. Solving the first part of the problem, we use a method of
specifying s.a. extensions by (asymptotic) s.a. boundary conditions. Solving
spectral problems, we follow the Krein's method of guiding functionals. This
work is a continuation of our previous works devoted to Coulomb, Calogero, and
Aharonov-Bohm potentials.Comment: 31 pages, 1 figur
Coherent State Quantization and Moment Problem
Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion
New solutions of relativistic wave equations in magnetic fields and longitudinal fields
We demonstrate how one can describe explicitly the present arbitrariness in
solutions of relativistic wave equations in external electromagnetic fields of
special form. This arbitrariness is connected to the existence of a
transformation, which reduces effectively the number of variables in the
initial equations. Then we use the corresponding representations to construct
new sets of exact solutions, which may have a physical interest. Namely, we
present new sets of stationary and nonstationary solutions in magnetic field
and in some superpositions of electric and magnetic fields.Comment: 25 pages, LaTex fil
Dynamical noncommutativity
The model of dynamical noncommutativity is proposed. The system consists of
two interrelated parts. The first of them describes the physical degrees of
freedom with coordinates q^1, q^2, the second one corresponds to the
noncommutativity r which has a proper dynamics. After quantization the
commutator of two physical coordinates is proportional to the function of r.
The interesting feature of our model is the dependence of nonlocality on the
energy of the system. The more the energy, the more the nonlocality. The
lidding contribution is due to the mode of noncommutativity, however, the
physical degrees of freedom also contribute in nonlocality in higher orders in
\theta.Comment: published versio