# 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.

## References

SHOWING 1-10 OF 15 REFERENCES

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

- Mathematics
- 2004

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

- Mathematics
- 2009

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

- Physics
- 1976

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

- Mathematics
- 1961

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

- Mathematics
- 1951

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…

### Scattering theory of waves and particles

- Physics
- 1966

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

- PhysicsNature
- 1947

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

- PhysicsNature
- 1969

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

- PhysicsNature
- 1975

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