2015/02/02 by E. I. Jafarov, A. M. Jafarova, J. Van der Jeugt · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.DS #math.MP
paper · pdf · doi:10.1088/1742-6596/597/1/012047
Contribution to the 30th International Colloquium on Group Theoretical Methods in Physics (Ghent, Belgium, 2014). To be published in Journal of Physics: Conference Series
arxiv created 2015/02/02 · arxiv updated 2015/06/23
We define a new algebra, which can formally be considered as a \cal C\cal P deformed \mathfraksu(2) Lie algebra. Then, we present a one-dimensional quantum oscillator model, of which the wavefunctions of even and odd states are expressed by Krawtchouk polynomials with fixed p=1/2, K2n(k;1/2,2j) and K2n(k-1;1/2,2j-2). The dynamical symmetry of the model is the newly introduced \mathfraksu(2)_\cal C\cal P algebra. The model itself gives rise to a finite and discrete spectrum for all physical operators (such as position and momentum). Among the set of finite oscillator models it is unique in the sense that any specific limit reducing it to a known oscillator models does not exist.