Abstract
The number of bound states in a standard rectangular potential well depends on the potential depth and width. In an impenetrable one-dimensional rectangular potential well, there are infinite bound states. In this work we study a non-Hermitian Riesz-Feller kinetic energy; i.e., the second-order derivative of the standard kinetic energy operator is replaced by a fractional, -order derivative. We show that for a particle in an impenetrable one-dimensional rectangular potential well contains a finite number of bound states and an infinite number of metastable decaying states. The transitions from bound states to metastable decaying states occur at values that correspond to exceptional points, for which two bound states coalesce. Our findings indicate that one can describe a transition of highly excited bound states to metastable decaying states, for example due to the interactions of atoms and molecules with the environment, by using the Riesz-Feller kinetic energy operator rather than the standard one.
1 More- Received 27 August 2018
DOI:https://doi.org/10.1103/PhysRevA.98.042110
©2018 American Physical Society