# A direct method for the low energy scattering solution of delta shell potentials

@article{Erman2021ADM, title={A direct method for the low energy scattering solution of delta shell potentials}, author={Fatih Erman and Sema Seymen}, journal={The European Physical Journal Plus}, year={2021}, volume={137} }

A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed, and the results are compared with the one using the standard partial wave analysis developed for potentials with rotational symmetry. The formulation is presented in momentum space, and the scattering solutions are obtained by considering the elementary use of distributions. In this approach, the outgoing boundary conditions are imposed explicitly in contrast to…

## References

SHOWING 1-10 OF 41 REFERENCES

### Quantum mechanics in momentum space: An illustration

- Physics
- 1975

The formulation of quantum‐mechanical problems in momentum space, which is largely ignored in traditional courses but is used in research, is discussed. In particular, the formulation of scattering…

### Introduction to Quantum Mechanics

- PhysicsNature
- 1945

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special…

### 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…

### Quantum scattering by a spherical barrier with an arbitrary coupling strength

- Physics, MathematicsPhysica Scripta
- 2021

A solution to the Lippmann-Schwinger equation for the scattering of a plane wave by a spherical barrier is presented. The spherical barrier is described by a boundary-wall with coupling constant γ =…

### The Schrödinger particle on the half-line with an attractive $$\delta $$-interaction: bound states and resonances

- MathematicsThe European Physical Journal Plus
- 2021

In this paper, we provide a detailed description of the eigenvalue E D ( x 0 ) ≤ 0 (respectively, E N ( x 0 ) ≤ 0) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the…

### Exact solution to Lippmann-Schwinger equation for a circular billiard

- MathematicsJournal of Mathematical Physics
- 2018

We present an exact solution to the Lippmann-Schwinger equation for a two-dimensional circular billiard. After diagonalizing an integral operator whose kernel is a zeroth order Hankel function of…

### On scattering from the one-dimensional multiple Dirac delta potentials

- Physics
- 2018

In this paper, we propose a pedagogical presentation of the Lippmann–Schwinger equation as a powerful tool, so as to obtain important scattering information. In particular, we consider a…

### An analytical example of renormalization in two‐dimensional quantum mechanics

- Physics
- 1991

As a concrete example of the idea of renormalization, quantum mechanical scattering of particles by a two‐dimensional delta‐function potential is considered. The renormalization of the scattering…