Quantum mechanics on a circle with a finite number of α-uniformly distributed points

Won Sang Chung, Ilyas Haouam, Hassan Hassanabadi

Published 2023-04-02Version 1

In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete angular momentum operators and Hermitian Hamiltonian on a circle with d {\alpha}-distributed discrete angles are constructed. The energy levels are computed for a free particle on a circle where the wave function is defined in the d {\alpha}-distributed discrete angles.