The su(2) Krawtchouk oscillator model under the CP deformed symmetry

30th International Colloquium on Group Theoretical Methods in Physics

Jafarov, E.I.^1 ; Jafarova, A.M.^2 ; Van Der Jeugt, J.^3

Institute of Physics, Azerbaijan National Academy of Sciences, Javid av. 33, Baku

AZ-1143, Azerbaijan^1

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan^2

Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281-S9, Gent

B-9000, Belgium^3

关键词: Discrete spectrum;    Dynamical symmetry;    Krawtchouk polynomials;    Lie Algebra;    Oscillator model;    Quantum oscillators;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012047/pdf
DOI  :  10.1088/1742-6596/597/1/012047

来源: IOP

【 摘 要 】

We define a new algebra, which can formally be considered as a CP deformed su(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 su(2)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.