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The WKB approximations in the calculation of the energy levels of the mixed harmonic-quartic oscillator are presented by using Miller and Good's modified version of this method. The results indicate that very close energy eigenvalues in comparison with the exact calculation results given by Chan, SteIman, and Thompson can be obtained with the exception of the ground state. If the harmonic oscillator is chosen as a base, the Miller and Good method coincides with the ordinary WKB method. If the quartic oscillator is used as a base, their method gives better eigenvalues than the ordinary WKB method does.

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,, the component of -iV in the direction of the field; J,, the component of xXp+s; and Ro2, theoperator 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.

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