• Corpus ID: 119625924

Delta-like singularity in the Reduction of the Laplace Equation for Spherical Coordinates and the Validity of Radial Schrodinger Equation

@article{AKhelashvili2010DeltalikeSI,
  title={Delta-like singularity in the Reduction of the Laplace Equation for Spherical Coordinates and the Validity of Radial Schrodinger Equation},
  author={Anzor A.Khelashvili and Teimuraz P. Nadareishvili},
  journal={arXiv: Mathematical Physics},
  year={2010}
}
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. 
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References

SHOWING 1-10 OF 15 REFERENCES

On the resolvent and spectral functions of a second order differential operator with a regular singularity

We consider the resolvent of a second order differential operator with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in…

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…

Conditions on wave functions derived from operator domains

Conditions on wave functions that are eigenvectors often have a mathematical rather than a physical basis; they are required simply because an eigenvector of an operator must be in the domain of that…

Theory of linear operators in Hilbert space

linear operators in hilbert spaces | springerlink abstract. we recall some fundamental notions of the theory of linear operators in hilbert spaces which are required for a rigorous formulation of the…

Fundamental properties of Hamiltonian operators of Schrödinger type

Introduction. The fundamental quality required of operators representing physical quantities in quantum mechanics is that they be hypermaximal(l) or self-adjoint(2) in the strict sense employed in…

Electron capture and scaling anomaly in polar molecules

Scattering theory of waves and particles

Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to…

The Principles of Quantum Mechanics

IT is now twenty years since the theory of quantum mechanics was founded, and not much less since the first edition of Dirac's book was published. Ever since, it has been a classic of scientific…

Classical Electrodynamics

Electrodynamics of Particles and PlasmasBy P. C. Clemmow and J. P. Dougherty. (Addison-Wesley Series in Advanced Physics.) Pp. ix + 457. (Addison-Wesley London, September 1969.) 163s.

Quantum mechanics

Quantum Mechanics for Organic Chemists.By Howard E. Zimmerman. Pp. x + 215. (Academic: New York and London, May 1975.) $16.50; £7.90.