Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

9 Self - adjoint extensions and spectral analysis in Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential αx−2 . Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in o...

Weyl Function and Spectral Properties of Self-adjoint Extensions

Self-adjoint Extensions of Restrictions

We provide, by a resolvent Krĕın-like formula, all selfadjoint extensions of the symmetric operator S obtained by restricting the self-adjoint operator A : D(A) ⊆ H → H to the dense, closed with respect to the graph norm, subspace N ⊂ D(A). Neither the knowledge of S∗ nor of the deficiency spaces of S is required. Typically A is a differential operator and N is the kernel of some trace (restric...

the stady and analysis of rice agroclimatology in lenjan

the west of esfahan province, iran, is one of the most important agricultural areas throughout the country due to the climate variability and life-giving water of zayanderood river. rice is one of the major and economic crops in this area. the most important climatic elements in agricultural activities which should be considered include temperature, relative humidity, precipitation and wind. so...

Self - adjoint extensions and Signature Change

We study the selfadjoint extensions of the spatial part of the D'Alembert operator in a spacetime with two changes of signature. We identify a set of boundary conditions, parametrised by U (2) matrices, which correspond to Dirichlet boundary conditions for the fields, and from which we argue against the suggestion that regions of signature change can isolate singularities.