An alternate way to calculate magnetic resonance for nuclei of arbitrary spin values

Although most textbooks only treat the magnetic resonance for spin ½ particles, which applies equally well for electron paramagnetic resonance and for magnetic resonance of spin ½ nuclei, in his 1966 book, Gottfried solved the Schrödinger equation for a general spin s particle in both a constant B₀ and a perpendicular oscillating magnetic field B_⊥cos(ωt) by transforming to a rotating reference frame. Here we provide a simpler procedure that extends the simpler solution for spin ½ particles to higher spin states. We first transform the amplitudes of the components of the spin vector to effective remove the time dependence of the effective Hamiltonian. Then, we diagonalize that effective Hamiltonian by a unitary transformation that changes the basis of the spin vector. Taking the time derivative of that Schrödinger equation then leads to a second order differential equation for each vector component, each equation of which has the form of a classical harmonic oscillator. The eigenvalues, eigenvectors, and resonance frequencies for each spin state can thereby be calculated precisely, and the eigenvalues and resonance frequencies follow a simple pattern arbitrary spin s. We will compare our results with those of Gottfried for s values up to 3.