- #1
lelouch_v1
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- TL;DR Summary
- Couldn't find the 8 eigenvalues of the problem
I was reading a paper on Radical-Pair mechanism (2 atoms with 1 valence electron each) and the author used the hyperfine hamiltonian and found the following eigenvalues: a/4 (doubly degenerate) , a/4±B , (-a-2B±2√(A^2+B^2)) , (-a+2B±2√(A^2+B^2))
What i used was the eigenvalue equation where ψ is a singlet and a triplet state, i.e. Using these states, i was able to get the first four eigenvalues. Since there are eight eigenvalues, should i right the terms in the hamiltonian as tensor products? Also, since I is the nuclear spin operator, do i take it always as 1/2 when in the z-direction, since i suppose that the nucleus is a hydrogen atom with one proton? Can i write the term in terms of the annihilation and creation operators, i.e. or is it wrong?
P.S.: In the hamiltonian, the subscript D is used for Donor and the subscript A for Acceptor.
What i used was the eigenvalue equation
P.S.: In the hamiltonian, the subscript D is used for Donor and the subscript A for Acceptor.