Renormalization of expansions for Regge trajectories of the Schr\"odinger equation

A recursion technique for the renormalization of semiclassical expansions for the Regge trajectories of bound states of the Schr\"odinger equation is developed. As an application of the proposed technique, the two-parameter renormalization scheme of the Regge trajectories for the bound states in the Martin potential is considered.Comment: 5 pages, no figure

Regge trajectories of the Klein-Gordon equation with non-minimal interaction

A semiclassical method of deriving Regge trajectories for the bound states of the Klein-Gordon equation with the interaction introduced in a non-minimal way is proposed. The method is applied to construction of the quarkonium Regge trajectories. It is found that under the relativistic generalization of the Cornell potential the Regge trajectories of charmonium are in the same good agreement with experimental data for introducing the confinement part of potential either in the minimal, or non-minimal way.Comment: 8 pages, 1 figur

Relativistic wave equation for one spin-1/2 and one spin-0 particle

A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with the Lorentz-scalar and Lorentz-vector potential interactions for the system of one spin-1/2 and one spin-0 particle with unequal masses is constructed.Comment: Talk given at International School-Seminar "New physics and QCD at external conditions" (Dniepropetrovsk, Ukraine, May 3-6, 2007); 8 pages; prepared for publication in Proceeding

A new approach to the logarithmic perturbation theory for the spherical anharmonic oscillator

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator are considered.Comment: Submitted to Journal of Physics A: Math. and Ge

The logarithmic perturbation theory for bound states in spherical-symmetric potentials via the ℏ\hbar-expansions

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As examples, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator and the Debye potential are considered.Comment: Talk given at International School-Seminar "New physics and QCD at external conditions" (Dniepropetrovsk, Ukraine, May 3-6, 2007); 11 pages; prepared for publication in Proceeding

Perturbation theory for sextic doubly anharmonic oscillator

A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic doubly anharmonic oscillator is investigated. The recursion technique for deriving renormalized perturbation expansions is offered

A recursion technique for deriving renormalized perturbation expansions for one-dimensional anharmonic oscillator

A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $\hbar$-expansions and suitable quantization conditions, the recursion formulae obtained have the same simple form both for ground and excited states and can be easily applied to any renormalization scheme. As an example, the renormalized expansions for the sextic anharmonic oscillator are considered.Comment: 9 pages, LaTe

A new two-body relativistic potential model for pionic hydrogen

The new potential model for pionic hydrogen, constructed with the employment of the two-body relativistic equation, is offered. The relativistic equation, based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one, describes the effect of the proton spin and anomalous magnetic moment in accordance with the results of the quantum electrodynamics. Within this approach, using the experimental data on the strong energy level shift and width of the $1s$ state in pionic hydrogen as input, the pion-nucleon scattering lengths have been evaluated to be $a_{\pi^{-}p}=0.0860(6)m_{\pi}^{-1}$ and $a_{\pi^{0}n}=-0.1223(19)m_{\pi}^{-1}$.Comment: 14 pages, no figure

A new perturbation technique for eigenenergies of the screened coulomb potential

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem of the radial Shrodinger equation with the screened Coulomb potential is developed. Based upon h-expansions and new quantization conditions a novel procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained

Energy spectrum of the Dirac oscillator in the Coulomb field

The spectrum of the Dirac oscillator perturbed by the Coulomb potential is considered. The Regge trajectories for its bound states are obtained with the method of $\hbar$-expansion. It is shown that the split of the degenerate energy levels of the Dirac oscillator in the Coulomb field is approximately linear in the coupling constant.Comment: 3 pages, 1 figure; published in proceedings of International Conference on Mathematical Methods in Electromagnetic Theory (MMET*06), Kharkiv, 26-28 June 2006, pp. 554-556; citation correcte