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## Homework Statement

The hamiltonian of a spin in a magnetic field is given by:

[tex]\hat{H} = \alpha\left( B_{x}\hat{S_{x}} + B_{y}\hat{S_{y}} + B_{z}\hat{S_{z}}\right)[/tex]

where [itex]\alpha[/itex] and the three components of

**B**all are constants.

Question: Compute the energies and eigenstates of the spin.

## Homework Equations

[tex]\hat{S_{x}} = \frac{\hbar}{2} \left[ \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right][/tex]

[tex]\hat{S_{y}} = \frac{\hbar}{2} \left[ \begin{array}{cc} 0 & -i \\ i & 0 \end{array} \right][/tex]

[tex]\hat{S_{z}} = \frac{\hbar}{2} \left[ \begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array} \right][/tex]

## The Attempt at a Solution

.. I don't know how or where to start