Deformed supersymmetric quantum mechanics with spin variables

We quantize the one-particle model of the $SU\left(2|1\right)$ supersymmetric multi-particle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter $m$ and $SU\left(2\right)$ spin $q\in (Z_{>0}$, $1/2+Z_{⩾0})$. It is found that the states at the fixed energy level form irreducible multiplets of the supergroup $SU\left(2|1\right)$. Also, the hidden superconformal symmetry $OSp\left(4|2\right)$ of the model is revealed in the classical and quantum cases. We calculate the $OSp\left(4|2\right)$ Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed $q$ are unified into an irreducible $OSp\left(4|2\right)$ multiplet.