- #1

Anton02

- 1

- 0

- Homework Statement
- Given the Spin Operator $$\hat{\vec{S}}=\frac{\hbar}{2}\hat{\vec{\sigma}}$$ with the Pauli matrices $$\hat{\vec{\sigma}}$$ calculate the Normalizationconstant A for the given Spinstate $$\chi$$

- Relevant Equations
- $$\chi=A\begin{pmatrix}

3i\\

4

\end{pmatrix}$$

$$\sigma_x=\begin{pmatrix}

0 & 1\\

1 & 0

\end{pmatrix}$$

$$\sigma_y=\begin{pmatrix}

0 & -i\\

i & 0

\end{pmatrix}$$

$$\sigma_z=\begin{pmatrix}

1 & 0\\

0 &-1

\end{pmatrix}$$

I don't really know where to begin.

1. idea: For a spatial wave funtion I'd have to calculate the integral over dxdydz for -inf to +inf. But that doesn't seem very reasonable to me here.

$$\int \chi dxdydz=\int A\begin{pmatrix}

3i\\

4

\end{pmatrix} dxdydz$$

Do have to substitute dxdydz with something and get the pauli matrizes involved?

2. idea: If I treat the spinstate like a regular vector the norm would just be $$\sqrt{3i^2+4^2}=\sqrt{16-9}=\sqrt{5}$$. But can I treat a spinstate like this?

1. idea: For a spatial wave funtion I'd have to calculate the integral over dxdydz for -inf to +inf. But that doesn't seem very reasonable to me here.

$$\int \chi dxdydz=\int A\begin{pmatrix}

3i\\

4

\end{pmatrix} dxdydz$$

Do have to substitute dxdydz with something and get the pauli matrizes involved?

2. idea: If I treat the spinstate like a regular vector the norm would just be $$\sqrt{3i^2+4^2}=\sqrt{16-9}=\sqrt{5}$$. But can I treat a spinstate like this?