- #1

Heimisson

- 44

- 0

## Homework Statement

A particle with spin 1/2 and magnetic moment is in a magnetic field B=B_0(1,1,0). At time t=0 the particle has the spin [tex]1/2 \hbar[/tex] in the z direction.

i) Write the hamiltonian

**with respect to the basis that is defined by the eigenvectors**of [tex]\widehat{S}_z[/tex]

## Homework Equations

[tex]\widehat{S}_z = \hbar /2

\left(

\begin{array}{ c c }

1 & 0 \\

0 & -1

\end{array} \right) [/tex]

## The Attempt at a Solution

So finding the hamiltonian is trivial:

[tex]H=-\gamma \textbf{B} \cdot \textbf{S} =

= B_0 \hbar /2

\left(

\begin{array}{ c c }

0 & 1-i \\

1+i & 0

\end{array} \right) [/tex]

if my calculations are right. But what I don't really don't understand is what I wrote in the bold font. I thought I had to find the matrix A so:

if:

[tex]B=

\left(

\begin{array}{ c c }

0 & 1-i \\

1+i & 0

\end{array} \right)[/tex]

[tex]A \widehat{S}_z = B \Rightarrow A = B \widehat{S}_z^{-1} [/tex]

but this is really just a shot in the dark I'm not really sure why I should do this.

It would be great if someone could shed some light on this I'm sort of rusty in linear algebra of finite vectors.