Quantum superconformal model in $(1,2)$ space

A Lagrangian invariant with respect to superconformal transformations in $(1,2)$ superspace is proposed. An exact solution of the system of nonlinear equations is obtained for interacting Bose and Fermi fields. Both the classical and the quantum aspects of the problem are considered. The complete spectrum of quantum states of the system described by the proposed Lagrangian is constructed by a generalization of the method developed by de Alfaro, Fubini, and Furlan.