- Problem Statement
- I have a situation with a spin 1/2 particle in a couple of magnetic fields (one - Bo - in the Z direction, and another - Γo - in the X direction). I found the energy eigenvalues for the system, but I don't know how to mount the time-dependent state vector, χ(t). I need this to determine the expected values for Sx, Sy and Sz. (It's a problem inspired in the Example 4.3 of the Griffiths book: Introduction to Quantum Mechanics - Chapter 4 -)
- Relevant Equations
- The Hamiltonian in the matrix form (I guess it is made by the relation H = -γ.Bo.Sz - γ.Γo.Sx); Pauli spin matrices; some other relations in the Chapter 4 of the book.
I just tried to find the eigenvalues (for the energy), obtaining E = ±(γħ.√(Bo² + Γo²))/2 and the corresponding eigenvectors for the H matrix. But I don't know what to do to create de state vector χ.