- #1

- 1,868

- 0

## Homework Statement

Hi all.

I have the following state at t=0 in a 3D Hilbert-space (it is in the eigenspace of the 3x3 Hamiltonian):

[tex]

\left| \psi \right\rangle = \frac{1}{{\sqrt 2 }}\left| \psi \right\rangle _1 + \frac{1}{2}\left| \psi \right\rangle _2 + \frac{1}{2}\left| \psi \right\rangle _3.

[/tex]

Now I have an operator representing an observal given by:

[tex]

\hat A = \left( {\begin{array}{*{20}c}

1 & 0 & 0 \\

0 & 0 & 1 \\

0 & 1 & 0 \\

\end{array}} \right)

[/tex]

I have to find the possible eigenvalues of A and the corresponding probabilities.

## The Attempt at a Solution

The possible eigenvalues of A are easy. I am more concerned about the probabilities. I reasoned that they are the same, because the above state at t=0 is

**independent**of the Hilbert space in is written in. So it will look the same if I write it in the eigenspace of A, but the unit-vectors (i.e. the possible states) are now different.

So my attempt: The probabilities are the same, i.e. 1/2, 1/4 and 1/4. Can you confirm this?

Thanks in advance.

Best regards,

Niles.