Multi-layer evolution schemes for the finite-dimensional quantum systems in external fields

The operator-difference multi-layer (ODML) schemes for solving the time-dependent Schrödinger equation (TDSE) till six order accuracy by a time step are presented. The reduced schemes for solving a set of the coupled TDSE’s are devised by using a set of appropriate basis angular functions and a finite element method with respect to a hyper-radial variable. Convergence by a number of the basis functions and efficiency of the numerical schemes are demonstrated in the case of an exactly solvable model of the two-dimensional oscillator in time-depended electric fields.     

High accuracy energy-level calculations of the rotational-vibrational weakly bound states of ddμ and dtμ mesic molecules

Calculations are performed of the nonrelativistic energies $\text{E}{}_{\mathrm{JV}}$ of rotational-vibrational weakly bound states J = ν = 1 of ddμ and dtμ mesic molecules: $\text{E}{}_{11}\text{(}\text{dd}\text{μ) = ? 1.956}\text{eV}$ and $\text{E}{}_{11}\text{(}\text{dt}\text{μ) = ? 0.656}\text{eV}$ with an accuracy of 0.001 eV. With the relativistic effects and nuclear finite size corrections taken into account the result is: $\text{E}{}_{11}\text{(}\text{dd}\text{μ) = ? 1.946}\text{eV}$ and $\text{E}{}_{11}\text{(}\text{dt}\text{μ) = ? 0.634}\text{eV}$.     

A generalized adiabatic approach to exotic three-body systems

A generalized adiabatic approach providing the asymptotic separation of the fast and slow variables for the three-body muonic scattering problem is considered. A uniform classification scheme of the different adiabatic bases for some typical three-body Coulomb systems is discussed. The estimations of the cross section of the elastic scattering process (t¯p) _n=1+d(t¯p)_n=1+d are presented.     

Adiabatic approach to the problem of a quantum well with a hydrogen-like impurity

An adiabatic method is presented for solving a boundary discrete spectrum problem for a parabolic quantum well and a rectangular quantum well with infinitely-high walls in the presence of a hydrogen-like impurity. The upper and lower bounds for the energy of the ground state of the systems are obtained under the conditions of the shift of the Coulomb center in a given range of the parameter with respect to earlier variational estimates. The comparison of the rate of convergence of the adiabatic expansion of the solution in parametric bases in the cylindrical and spherical coordinates is carried out.     

Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

In the effective mass approximation for electronic (hole) states of a spheroidal quantum dot with and without external fields the perturbation theory schemes are constructed in the framework of the Kantorovich and adiabatic methods. The eigenvalues and eigenfunctions of the problem, obtained in both analytical and numerical forms, were applied for the analysis of spectral and optical characteristics of spheroidal quantum dots in homogeneous electric fields.     

Solution of Quantum Mechanical Problems Using Finite Element Method and Parametric Basis Functions

New computational schemes, symbolic-numerical algorithms and programs implementing the high-accuracy finite element method (FEM) for the solution of quantum mechanical boundary-value problems (BVPs) are reviewed. The elliptic BVPs in 2D and 3D domains are solved using the multivariable FEM and Kantorovich method using parametric basis functions. We demonstrate and compare the efficiency of the proposed calculation schemes, algorithms, and software by solving the benchmark BVPs that describe the scattering on a barrier and a well, the bound states of a helium atom, and the quadrupole vibration in a collective nuclear model.     

Fine and hyperfine structure of antiprotonic helium

We consider the fine and hyperfine splitting of the energy levels of antiprotonic helium pHe⁺ in highly excited rotational states in connection with the interpretation of the recently discovered delayed annihilation of antiprotons in helium, based on the Condo model.     

μ-capture and ortho-para transitions in the muonic molecule ppμ

The capture of a muon by protons at different hydrogen densities is considered. More precise values of γ-factors for ortho- and para-states of the muonic molecule ppμ are obtained: 2γ_o = 1.009±0.001 and 2γ_p = 1.143±0.001. Relativistic effects are taken into account in the muonic molecule, and the rate of ortho-para transitions λ_op = (7.1±1.2) × 10⁴s^?1, caused by these effects, is calculated. With this value of λ_op the μ-capture rate in liquid hydrogen is found to be Λ_c = (490±10)s^?1 that is in agreement with the value Λ_c = 460±20 s^? recently measured by the Saclay-CERN-Bologna collaboration.