  Kramers degeneracy theorem is one of the basic results in quantum mechanics.
According to it, the time-reversal symmetry makes each energy level of a
half-integer spin system at least doubly degenerate, meaning the absence of
transitions or scatterings between degenerate states if the Hamiltonian does
not depend on time explicitly. We generalize this result to the case of
explicitly time-dependent spin Hamiltonians. We prove that for a spin system
with the total spin being a half integer, if its Hamiltonian and the evolution
time interval are symmetric under a specifically defined time reversal
operation, the scattering amplitude between an arbitrary initial state and its
time reversed counterpart is exactly zero. We also discuss applications of this
result to the multistate Landau-Zener (LZ) theory.
