In this study, we have chosen the spatial confinement parabolic on semiconductor quantum wire with applied magnetic field. Thus, electrons are confined in zone where two parabola overlapped by using single step between two parabolic potential. The energy eigenvalues and wave functions of electrons under this double parabolic confinement are obtained by solving Schrödinger equation in the framework of asymptotic iteration method. The creation and annihilation operators for the radial wave functions are constructed by using factorization method, it is shown that these ladder operators satisfy the commutation relations for the SU(1,1) group. Closed analytical expressions for the matrix elements of  and  are obtained and the coherent state analysis for the system are carried out.