• Raising and lowering operators for quantum billiards

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/089/03/0035

• # Keywords

Eigenfunctions; integrable billiards; nonseparable systems

• # Abstract

For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as $m$, $n$, the index which represents a class is $c = m$ mod $kn$ for a natural number, $k$. We show here that the entire tower of states can be generated from an initially given state by the application of the operators introduced here. Thus, these operators play the same role for billiards as raising and lowering operators in angular momentum algebra.

• # Author Affiliations

1. Complexity Science Group, University of Calgary, Calgary, AB T2N 1N4, Canada
2. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
3. Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400 094, India

• # Pramana – Journal of Physics

Volume 96, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019