Logarithmic Potential Model of Quigg and Rosner as a Generalization of Naive Quark Model

Exploiting the explicit mass formulae for logarithmic potential model of Quigg and Rosner it is shown that at least on the level of mass-relations this model reproduces the naive quark model relations and generalizes the last one in case of highly non-trivial potential. Generalization includes the relations for higher values of orbital quantum numbers. In particular, preditions for recently discovered atom-like P-states are no worse than for any other potential models.The advantage consists in simplicity of approach.Comment: 5 page

Unusual Bound States in QFT Models

Homogeneous Bethe-Salpeter equation for simplest Wick-Cutkosky model is studied in the case when the mass of the two-body system is more then the sum of constituent particles masses. It is shown that there is always a small attraction between the like-sigh charged particles as a pure relativistic effect. If the coupling constant exceeds some critical values there arise discrete levels.The situation here is analogous to the so-called "abnormal" solutions.The signature of the norm of these discrete states coincides with the "time-parity".The states with the negative norms can be excluded from the physical sector-the one-time (quasipotential) wave-function corresponding to them vanishes identically.However the positive norm states survive and contribute to the total Green function (and the S-matrix) with the proper sign.Comment: 12 pages, 4 fugure

On the Abnormal Type Anomalous Solutions of Quasipotential Equations

It is shown that there exist solutions of the quasipotential equations exhibiting the abnormal type behaviour of the Bethe-Salpeter equation.Comment: 8 pages, LaTex, no figure

Some Problems of Self-Adjoint Extension in the Schrodinger equation

The Self-Adjoint Extension in the Schrodinger equation for potentials behaved as an attractive inverse square at the origin is critically reviewed. Original results are also presented. It is shown that the additional solutions must be retained for definite interval of parameters, which requires performing of Self-Adjoint Extension necessarily. The "Pragmatic approach" is used and some of its consequences are considered for wide class of transitive potentials. The problems of restriction of Self-Adjoint Extension parameter are also discussed. Various relevant applications are presented as well.Comment: 23 pages,submitted to J.Phys.

Generating functional of ChPT at one loop for non-minimal operators

The divergent part of the one-loop effective action in Chiral Perturbation Theory with virtual photons has been evaluated in an arbitrary covariant gauge. The differential operator, that emerges in the functional determinant, is of a non-minimal type, for which the standard heat kernel methods are not directly applicable. Both SU(2) and SU(3) cases have been worked out. A comparison with existing results in the literature is given.Comment: 14 page

Supersymmetry in the Dirac equation for generalized Coulomb potential

We propose a symmetry of the Dirac equation under the interchange of signs of eigenvalues of the Dirac's $K$ operator. We show that the only potential which obeys this requirement is the Coulomb one for both vector and scalar cases. Spectrum of the Dirac Equation is obtained algebraically for arbitrary combination of Lorentz-scalar and Lorentz-vector Coulomb potentials using the Witten's Superalgebra approach. The results coincides with that, known from the explicit solution of the Dirac equation.Comment: 10 pages. Submitted to Phys. Rev.

Delta-like singularity in the Radial Laplace Operator and the Status of the Radial Schrodinger Equation

By careful exploration of separation of variables into the Laplacian in spherical coordinates, we obtain the extra delta-like singularity, elimination of which restricts the radial wave function at the origin. This constraint has the form of boundary condition for the radial Schrodinger equation.Comment: 8 page

Unexpected Delta-Function Term in the Radial Schrodinger Equation

Careful exploration of the idea that equation for radial wave function must be compatible with the full Schrodinger equation shows appearance of the delta-function while reduction of full Schrodinger equation in spherical coordinates. Elimination of this extra term produces a boundary condition for the radial wave function, which is the same both for regular and singular potentials.Comment: 5 page

Status of the Radial Schrodinger Equation

We show that equation for radial wave function in its traditional form is compatible with the full Schrodinger equation if and only if a definite additional constraint required. This constraint has a boundary condition form at the origin. Some of consequences are also discussed.Comment: 6 page

Once Again On the Klein Paradox

After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown, that the separation of angular variables and reduction to radial equation is possible by using standard methods in momentum space. The kernel of the obtained radial equation differs from that of spinless Salpeter equation in bounded regular factor. That is why the equation has solutions of confined type for infinitely increasing potential