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

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, K_2n(k; 1/2, 2j) and K_2n(k — 1; 1/2, 2j — 2). The dynamical symmetry of the model is the newly introduced su(2)_CP 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. (paper)