# Contact interactions and Kronig–Penney models in Hermitian and PT symmetric quantum mechanics

@article{Thompson2018ContactIA, title={Contact interactions and Kronig–Penney models in Hermitian and PT symmetric quantum mechanics}, author={Foster Thompson and Katherine Brown and Harsh Mathur and Kristin McKee}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2018}, volume={51} }

The delta function potential is a simple model of zero-range contact interaction in non-relativistic quantum mechanics in one dimension. The Kronig–Penney model is a one-dimensional periodic array of delta functions and provides a simple illustration of energy bands in a crystal. Here we investigate contact interactions that generalize the delta function potential and corresponding generalizations of the Kronig–Penney model within conventional and symmetric quantum mechanics. In conventional…

## One Citation

### Perturbative method for resolving contact interactions in quantum mechanics

- PhysicsPhysical Review A
- 2019

Long-range effective methods are ubiquitous in physics and in quantum theory, in particular. Furthermore, the reliability of such methods is higher when the nature of short-ranged interactions need…

## References

SHOWING 1-10 OF 40 REFERENCES

### Particle in a box in PT -symmetric quantum mechanics and an electromagnetic analog

- Physics
- 2013

In PT quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P…

### Making sense of non-Hermitian Hamiltonians

- Physics
- 2007

The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarantees that the energy…

### Bound states, scattering states, and resonant states in PT -symmetric open quantum systems

- Physics
- 2015

We study a simple open quantum system with a PT-symmetric defect potential as a prototype to illustrate general features of PT-symmetric open quantum systems; however, the potential could be mimicked…

### Delta-function potential with a complex coupling

- Mathematics, Physics
- 2006

We explore the Hamiltonian operator , where is the Dirac delta function and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a spectral singularity at . For Re(z) 0, H has…

### EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE

- Physics
- 1963

A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the…

### On the Similarity of Sturm–Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators

- Mathematics
- 2011

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to…

### Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry

- Mathematics
- 1998

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new…

### Tonks–Girardeau gas of ultracold atoms in an optical lattice

- PhysicsNature
- 2004

A theoretical prediction of the momentum distribution is made based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.

### Möbius structure of the spectral space of Schrödinger operators with point interaction

- Mathematics
- 2001

The Schrodinger operator with point interaction in one dimension has a U(2) family of self-adjoint extensions. We study the spectrum of the operator and show that (i) the spectrum is uniquely…