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Quantum mechanics of layers with a finite number of point perturbations

Pavel Exner K Nmcov

TBD mathscidoc:1910.43098

Journal of Mathematical Physics, 43, (3), 1152-1184, 2002.3
We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character of the model follows from the explicit form of the Hamiltonian resolvent obtained by means of Kreins formula. We prove the existence of bound states, demonstrate their properties, and find the on-shell scattering operator. Furthermore, we analyze the situation when the system is put into a homogeneous magnetic field perpendicular to the layer; in that case the point interactions generate eigenvalues of a finite multiplicity in the gaps of the free Hamiltonian essential spectrum.
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@inproceedings{pavel2002quantum,
  title={Quantum mechanics of layers with a finite number of point perturbations},
  author={Pavel Exner, and K Nmcov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125829234093627},
  booktitle={Journal of Mathematical Physics},
  volume={43},
  number={3},
  pages={1152-1184},
  year={2002},
}
Pavel Exner, and K Nmcov. Quantum mechanics of layers with a finite number of point perturbations. 2002. Vol. 43. In Journal of Mathematical Physics. pp.1152-1184. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125829234093627.
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