What is the expectation value of Sz for the ground state?

[shally]

Homework Statement

Kindly take a look at the attachment for the problem statement.

Homework Equations

Schrödinger Equation: H psi = E psi

The Attempt at a Solution

For Part A: H psi = E psi
S= 1/2
So energy of ground state is -1/2.K.H.hcross

Could you tell me if I am on the right track?

I have no idea on how to attempt Part B. Kindly help. Thank you.

 

[ideasrule]

For Part A: H psi = E psi
S= 1/2
So energy of ground state is -1/2.K.H.hcross

Yes, that's correct.

I have no idea on how to attempt Part B. Kindly help. Thank you.

Since the magnetic field has no component in the y or z directions, the Hamiltonian just extracts the x component of the spin and multiplies it by -KH. So eigenvectors of the Hamiltonian are eigenvectors of Sx.

However, you're looking for the expectation value of Sz. Can you write the ground state in terms of the spin states for the z direction?