In this work, the general nonrelativistic classical statistical theory presented in an earlier paper (J. Mod. Phys. 8, 786 (2017)) is applied in detail to the Euler angle and center-of-mass coordinates of an extended rigid body with arbitrary distributions of mass and electric charge. Results include the following: 1) The statistical theory spin angular momentum operators are independent of the body’s morphology;2) These operators obey the usual quantum commutation rules in a non-rotating center-of-mass (CM) reference frame, but left-handed rules in a rotating body-fixed CM frame;3) Physical boundary conditions on the Euler angle wavefunctions restrict all mixed spin wavefunctions to a superposition of half-odd-integer spin eigenstates only, or integer spin eigenstates only;4) Spin s eigenfunctions are also Hamiltonian eigenfuctions only if at least two of the body’s principal moments of inertia are equal;5) For a spin s body with nonzero charge density in a magnetic field, the theory automatically yields 2s+1 coupled wave equations, valid for any gyromagnetic ratio;and 6) For spin 1/2 the two coupled equations become a Pauli-Schrödinger equation, with the Pauli matrices appearing automatically in the interaction Hamiltonian.
展开▼
