870 research outputs found
Classical approach in quantum physics
The application of a classical approach to various quantum problems - the
secular perturbation approach to quantization of a hydrogen atom in external
fields and a helium atom, the adiabatic switching method for calculation of a
semiclassical spectrum of hydrogen atom in crossed electric and magnetic
fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's
approach to Stark problem, long-lived excited states of a helium atom recently
discovered with the help of Poincar section, inelastic
transitions in slow and fast electron-atom and ion-atom collisions - is
reviewed. Further, a classical representation in quantum theory is discussed.
In this representation the quantum states are treating as an ensemble of
classical states. This approach opens the way to an accurate description of the
initial and final states in classical trajectory Monte Carlo (CTMC) method and
a purely classical explanation of tunneling phenomenon. The general aspects of
the structure of the semiclassical series such as renormgroup symmetry,
criterion of accuracy and so on are reviewed as well. In conclusion, the
relation between quantum theory, classical physics and measurement is
discussed.Comment: This review paper was rejected from J.Phys.A with referee's comment
"The author has made many worthwhile contributions to semiclassical physics,
but this article does not meet the standard for a topical review"
The hydrogen atom in electric and magnetic fields : Pauli's 1926 article
The results obtained by Pauli, in his 1926 article on the hydrogen atom, made
essential use of the dynamical so(4) symmetry of the bound states. Pauli used
this symmetry to compute the perturbed energy levels of an hydrogen atom in a
uniform electric field (Stark effect) and in uniform electric and magnetic
fields. Although the experimental check of the single Stark effect on the
hydrogen atom has been studied experimentally, Pauli's results in mixed fields
have been studied only for Rydberg states of rubidium atoms in crossedfields
and lithium atoms in parallel fields.Comment: 11 pages, latex file, 2 figure
Finite Element Approximation of the Minimal Eigenvalue of a Nonlinear Eigenvalue Problem
Ā© 2018, Pleiades Publishing, Ltd. The problem of finding the minimal eigenvalue corresponding to a positive eigenfunction of the nonlinear eigenvalue problem for the ordinary differential equation with coefficients depending on a spectral parameter is investigated. This problem arises in modeling the plasma of radiofrequency discharge at reduced pressures. A necessary and sufficient condition for the existence of a minimal eigenvalue corresponding to a positive eigenfunction of the nonlinear eigenvalue problem is established. The original differential eigenvalue problem is approximated by the finite element method on a uniform grid. The convergence of approximate eigenvalue and approximate positive eigenfunction to exact ones is proved. Investigations of this paper generalize well known results for eigenvalue problems with linear dependence on the spectral parameter
On foundations of quantum physics
Some aspects of the interpretation of quantum theory are discussed. It is
emphasized that quantum theory is formulated in the Cartesian coordinate
system; in other coordinates the result obtained with the help of the
Hamiltonian formalism and commutator relations between 'canonically conjugated'
coordinate and momentum operators leads to a wrong version of quantum
mechanics. The origin of time is analyzed in detail by the example of atomic
collision theory. It is shown that for a closed system like the three-body (two
nuclei + electron) time-dependent Schroedinger equation has no physical meaning
since in the high impact energy limit it transforms into an equation with two
independent time-like variables; the time appears in the stationary
Schroedinger equation as a result of extraction of a classical subsystem (two
nuclei) from a closed three-body system. Following the Einstein-Rozen-Podolsky
experiment and Bell's inequality the wave function is interpreted as an actual
field of information in the elementary form. The relation between physics and
mathematics is also discussed.Comment: This article is extended version of paper: Solov'ev, E.A.:
Phys.At.Nuc. v. 72, 853 (2009
General solution of equations of motion for a classical particle in 9-dimensional Finslerian space
A Lagrangian description of a classical particle in a 9-dimensional flat
Finslerian space with a cubic metric function is constructed. The general
solution of equations of motion for such a particle is obtained. The Galilean
law of inertia for the Finslerian space is confirmed.Comment: 10 pages, LaTeX-2e, no figures; added 2 reference
Deformation Wave Hardening of Metallic Materials
The article deals with the machine parts hardening by means of deformation waves generated by the
impact system with a waveguide as an intermediary member. The conditions for the efficient use of impact
energy for elastoplastic deformation of the processed material and creation of the deep hardened surface
layer.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3638
Reconstruction of multiplicative space- and time-dependent sources
This paper presents a numerical regularization approach to the simultaneous determination of multiplicative space- and time-dependent source functions in a nonlinear inverse heat conduction problem with homogeneous Neumann boundary conditions together with specified interior and final time temperature measurements. Under these conditions a unique solution is known to exist. However, the inverse prob- lem is still ill-posed since small errors in the input interior temperature data cause large errors in the output heat source solution. For the numerical discretisation, the boundary element method combined with a regularized nonlinear optimization are utilized. Results obtained from several numerical tests are provided in order to illustrate the efficiency of the adopted computational methodology
Eigenvibrations of a beam with elastically attached load
Ā© 2016, Pleiades Publishing, Ltd.The nonlinear eigenvalue problem describing eigenvibrations of a beam with elastically attached load is investigated. The existence of an increasing sequence of positive simple eigenvalues with limit point at infinity is established. To the sequence of eigenvalues, there corresponds a system of normalized eigenfunctions. The problem is approximated by the finite element method with Hermite finite elements of arbitrary order. The convergence and accuracy of approximate eigenvalues and eigenfunctions are investigated
Computation of the minimum eigenvalue for a nonlinear Sturm-Liouville problem
Ā© 2014, Pleiades Publishing, Ltd. A condition for the existence of a minimum eigenvalue corresponding to a positive eigenfunction of the nonlinear eigenvalue problem for an ordinary differential equation is determined. The problem is approximated by a mesh scheme of the finite element method. The convergence of approximate solutions to exact ones is studied. Theoretical results are illustrated by numerical experiments for a model problem
Approximation of nonlinear spectral problems in a Hilbert space
Ā© 2015, Pleiades Publishing, Ltd. We study an eigenvalue problem with a nonlinear dependence on the parameter in a Hilbert space. We establish the existence of eigenvalues and eigenelements. The original infinite-dimensional problem is approximated by a problem in a finite-dimensional subspace. We investigate the convergence and accuracy of approximate eigenvalues and eigenelements
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