Stationary States of a Spin-1 Particle in a Constant Magnetic Field

Shay and Good's wave equation is solved for a spin-1 particle with arbitrary magnetic dipole moment. Simultaneous eigenfunctions of the following three operators are used: $p_z$, the component of $-i\nabla$ in the direction of the field; $J_z$, the component of x×p+s; and ${R_0}^2$, the operator for the square of the distance to the center of the orbit in the projection of the motion perpendicular to the field. Explicit formulas for the allowed energies in terms of the quantum numbers are found. Determination of the wave functions is reduced to a set of linear algebraic equations.