arXiv subjects
Publications and source records attributed to Le Van Hoang.
The scheme of isospin separation is suggested for the equation describing the five-dimensional 'charge-dyon' system in a non-Abelian SU(2) model. As a result, we obtain the Schrodinger equation for 'bare' particle, moving in Coulomb potential plus potential of five-dimensional Dirac monopole.
The Hurwits transformation is generalized by introducing three new variables called 'extra'. Interpretation of these extra variables allows us to establish relation between isotropic harmonic oscillator and five-dimensional hydrogen-like atom in 'electromagnetic' fields of various configurations. For the Schrodinger equations, the scheme of separation of extra variables is suggested.
The use of Levi-Civita transformation allows us to formulate the problem of two-dimensional screened donor states in a magnetic field as that of two-dimensional anharmonic oscillator. Therefore, the operator method can be directly used for the first problem and the exact solutions of Schrodinger equation are obtained correspondently. In our approach, wave-functions are constructed in the representation of annihilation and creation operators, which permits one to use purely algebraic method in further calculations of other characteristics. The considered problem is related to the motion of 2D electron gas in GaAs/AlGaAs multiple-quantum well structures with the presence of a magnetic field, which continues to provide new and fascinating phenomena.
Basing on the relation between the Coulomb Green function and the Green function of harmonic oscillator, the algebraic representation of the many-particle Coulomb Green function in the form of annihilation and creation operators is established. These results allow us to construct purely algebraic method for atomic calculations and thus to reduce rather complicated calculations of matrix elements to algebraic procedures of transforming the products of annihilation and creation operators to a normal form. Effectiveness of the constructed method is demonstrated through the example problem: the ground state of hydrogenic molecule. The calculation algorithm of this algebraic approach is simple and suitable for symbolic calculation programs, such as Mathematica, that widely enlarge the application field of the Coulomb Green function
Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The relativistic dynamical polarizability of hydrogen-like atoms is calculated and analysed.