  We construct a new version of the worldline SU(2|1) superspace as a
deformation of the standard N =4, d=1 superspace and show that it naturally
provides off- and on-shell description of general supersymmetric K\"ahler
oscillator model considered earlier at the classical level within the
Hamiltonian approach. The basic object is a generalized chiral SU(2|1), d=1
superfield with the off-shell field content (2, 4, 2). The frequency of the
oscillator and the strength of external magnetic field are defined by two
parameters: the contraction parameter $m$ and the new parameter $\lambda$ which
reflects the freedom in defining the chiral SU(2|1), d=1 superspace. We treat
both classical and quantum cases.

High Energy Physics - Theory