A New Kind of Shift Operators for Infinite Circular and Spherical Wells

A new kind of shift operators for infinite circular and spherical wells is identified. These shift operators depend on all spatial variables of quantum systems and connect some eigenstates of confined systems of different radii sharing energy levels with a common eigenvalue. In circular well, the momentum operators play the role of shift operators. The and operators, the third projection of the orbital angular momentum operator , and the Hamiltonian form a complete set of commuting operators with the SO(2) symmetry. In spherical well, the shift operators establish a novel relation between and .