Boundaries Of Spectral Clusters Research Articles

Semiclassical Asymptotics of the Spectrum of a Two-Dimensional Hartree Type Operator Near Boundaries of Spectral Clusters

Semiclassical Asymptotics of the Spectrum of a Two-Dimensional Hartree Type Operator Near Boundaries of Spectral Clusters

Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters

Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters

Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Lower Boundaries of Spectral Clusters

Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Lower Boundaries of Spectral Clusters

Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Upper Boundaries of Spectral Clusters

We study the Zeeman–Stark effect in the hydrogen atom located in an electromagnetic field by using irreducible representations of an algebra with the Karasev–Novikova quadratic commutation relations. The representations are associated with resonance spectral clusters near the energy level of the unperturbed hydrogen atom. We find asymptotics for a series of eigenvalues and corresponding asymptotic eigenfunctions near the upper boundaries of spectral clusters in the case of positive intensities of the electric field.

Asymptotics of the Spectrum and Quantum Averages of a Hartree Type Operator Near the Lower Boundaries of Spectral Clusters

We study the spectral problem for a two-dimensional Hartree type operator with smooth selfaction potential. We find asymptotic eigenvalues and eigenfunctions and construct an asymptotic expansion for quantum averages near the lower boundaries of spectral clusters.

Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters

The Zeeman—Stark effect for the hydrogen atom in an electromagnetic field is considered by using irreducible representations of an algebra with Karasev—Novikova quadratic commutation relations. The asymptotics of the series of eigenvalues and asymptotic eigenfunctions are obtained near the lower boundaries of the resonance spectral clusters, which are formed near the energy levels of the unperturbed hydrogen atom.

On the Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields Near the Upper Boundaries of Spectral Clusters

The problem of the Zeemann-Stark effect for the hydrogen atom in electromagnetic fields is considered using the irreducible representations of the Karasev-Novikova algebra with quadratic commutation relations. An asymptotics of the series of eigenvalues and the asymptotic eigenfunctions are obtained near the upper boundaries of resonance spectral clusters which are formed near the energy levels of an unperturbed hydrogen atom.

Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters

We consider the eigenvalue problem for a perturbed two-dimensional resonance oscillator. The excitation potential is given by a Hartree-type nonlinearity with a smooth self-action potential. We use asymptotic formulas for the quantum averages to obtain asymptotic eigenvalues and asymptotic eigenfunctions near the lower boundaries of spectral clusters which are formed near the energy levels of the unperturbed operator.

Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle

We consider the eigenvalue problem for the Hartree operator with a small parameter multiplying the nonlinearity. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundaries of spectral clusters formed near the energy levels of the unperturbed operator. Near the circle where the solution is localized, the leading term of the expansion is a solution of the two-dimensional oscillator problem.

Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters

In the eigenvalue problem for a perturbed two-dimensional oscillator, we suggest a method for constructing asymptotic solutions near the boundaries of spectral clusters by means of a new integral representation and study the issue of calculating the average values of differential operators on the solutions near the boundaries of the clusters.

Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators

The eigenvalue problem for the perturbed resonant oscillator is considered. A method for constructing asymptotic solutions near the boundaries of spectral clusters using a new integral representation is proposed. The problem of calculating the averaged values of differential operators on solutions near the cluster boundaries is studied.