Dear Wien2k users,
We are interested in calculation of expectation value of spin for a state |n,k>,
where n is the band index and k is the wave vector. For this purpose we have
slightly modified lapwdm program. The problem we are encountering is that the
expectation value of z-component of Pauli matrix (sigma_z) is not equal one.
Let us assume for simplicity spin-up state |n,k> and no spin-orbit coupling.
The expectation value for sigma_z we calculate as
sum_a ( rho_{n,k,a} sigma_z ) not= 1 (it is smaller then 1, typical
range 0.6-0.9)
where sum_a is the summation over atoms in unit cell.
1. Why we do not obtain for the state |n,k> expectation value equal one?
It is rather obvious that in this example <n,k| sigma_z |n,k> =1.
2. What is the density matrix normalization in this case?
rho_{n,k,a} is in this simple example 2x2 matrix having only up-up component,
which is given as Trace in orbital subspaces (sum for L=0,1,2,3) of given state
|n,k>.
Many thanks in advance,
Martin
[We are running Wien2k v9.1]
