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Pragmatic Self-adjoint Procedure in the Schrodinger Equation for the Inverse Square Potential
Anzor Khelashvili, Teimuraz Nadareishvili
The self-adjoint extension (SAE) procedure is considered in the Schrodinger equation for potentials behaving as an attractive inverse square at the origin of coordinates. This appr…
Self-adjoint extension procedure for a singular oscillator
Anzor Khelashvili, Teimuraz Nadareishvili
For a singular oscillator, the Schrodinger equation is obtained an equation of eigenvalues, and the dependence of energy on the self-adjoint extension parameter is established. It…
Comments about the boundary condition for reduced radial wave function in multi-dimensional equation
Anzor Khelashvili, Teimuraz Nadareishvili
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been of…
Generalized uncertainty relations in spherical coordinates
Anzor Khelashvili, Teimuraz Nadareishvili
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the dist…
Application of Modified Hypervirial and Ehrenfest Theorems and Some of its Consequences
Anzor Khelashvili, Teimuraz Nadareishvili
It is well-known that owing to the restricted character of the area additional surface terms emerge in the traditional form of hypervirial and/or Ehrenfest theorems. Especially, wh…
Hypervirial and Ehrenfest theorems in spherical coordinates: systematic approach
Anzor Khelashvili, Teimuraz Nadareishvili
Elaboration of some fundamental relations in three dimensional quantum mechanics is considered taking into account the restricted character of areas in radial distance. In such cas…