[en] A new iteration procedure for solution of the Schroedinger equation with arbitrary potential is proposed. Both the eigenvalues and eigenfunctions are represented in the form of a series which is well convergent under certain conditions. The solution of the K-dimensional Schroedinger equation within the proposed scheme reduces to a problem of the k-dimensional electrostatics. As an example potentials xsup(2n) (n=2,3,4) and m²x²+gx⁴ in an one-dimensional space are considered. It is shown that closed analytical expressions for corrections at all orders of the perturbation theory can be derived

[en] We show that the existence of algebraic forms of exactly solvable A-B-C-D, G₂, and F₄ Olshanetsky-Perelomov Hamiltonians allows one to develop algebraic perturbation theory, where corrections are computed by purely algebraic means. A classification of perturbations leading to such a perturbation theory based on the theory of representations of Lie algebras is given. In particular, this scheme admits an explicit study of anharmonic many-body problems. Some examples are presented

[en] A certain nonstandard approach to the problem of calculation of the spectrum in the nonrelativistic quantum mechanics is outlined. Along with simplicity and economy it is characterized by many abvantages as compared with traditional methods: in the cases when the traditional Rayleigh-Schroedinger perturbation theory (PT) can be realized, the suggested approach is algebraic and permits to analyse the properties of any correction, it provides the possibility to evaluate the accuracy of variational calculations and besides there natural arises from it the criterion of ''advisability'' of probe functions selection as for the procedure elaboration no knowledge of the whole spectrum of the unperturbed problem is required, there appears arbitrariness in the unperturbed problem selection which permits to construct the converging PT, the process of transition matrix elements calculation becomes algebraic. Numerous examples demonstrate approach possibilities which permit to easily calculate various PT corrections, confirm old calculations and obtain new results

[en] The problem of hydrogen atom placed in constant external magnetic field is studied. The properties of ordinary perturbation theory (in powers of the field) in the framework of a new approach proposed earlier are investigated. The ground state are considered in detailed while the excited states are discussed only in brief. It is shown that the ''wave function corrections'' with in this approach are simpler than within ordinary one and contain a finite number of harmonics with polynomial coefficients. Some coefficients of these polynomials are found explicitly

[en] It is shown that there exists for each exactly-soluble problem (in sense of Infeld-Hull factorization method) the associated quasi-exactly-soluble one, for which the first N-th eigenstates are known exactly. These problems contains some free parameters and the first N-th states form the N-sheet Rieman surface, which is separated from the whole spectral, infinitely-sheet - Riemann surface. In the limit N → ∞ the plaited eigenvalues are unplaited and the ordinary exactly-soluble problem appears

[en] Quasiclassical series of perturbation theory for ground energy state of anharmonxc oscillator with 0(2 n) symmetry and for the Gell-Mann-Low function of the scalar theory with strong nonlinearity with 0 (2 n) internal symmetry group are summed up. It is shown, that there exists the logarithmic singularity esup(1/g)Ei(-1/g) at g=0. Possible modifications due to the corrections of quasiclassical quautization are discussed

[en] The pp → Σ ⁺K⁺n and pp → YX reactions are examined in the framework of the reggesized single-pion exchange. It has been shown that the model can describe the Tryman-Young angle distributions for an exclusive reaction and represent the form and energy dependence of hyperon spectra for inclusive reactions. Scaling is predicted of NAL. The literature on experimental data for the πN → KY type reactions is presented

[en] The reactions pp→ΛX and pp→Σ⁺(Σ⁰)X are analyzed within the OPER model. It is shown that the model makes it possible to describe both the form and the energy dependence of the spectra. The onset of the scaling regime at NAL energies is predicted. The entire description is made in an absolute normalization

[en] A new perturbation theory for solution of the K-dimensional Schroedinger equation with arbitrary potential is proposed. It does not require the knowledge of the entire spectrum of the nonperturbed problem and gives closed expressions for the energy shifts. The procedure is a generalization of the variational method and permits to find its accuracy. Two dimensional nonsymmetric anharmonic oscillators are considered as an example

[en] Precision calculation of energies of several first states at d=2 and first 17 states at d=3 has been performed within the framework of a unique method based on ''nonlinearization'' method for d-dimension anisotropic an harmonic oscillator. Spectrum behaviour within the limit d → ∞ has been investigated and problems of the given approach accuracy have been studied. For the first time properties of nodal surfaces of the given task have been investigated. Routine perturbation theory in degrees of a perturbation parameter has been constructed for several first states