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## Homework Statement

I’m trying to derive a result from a book on quantum mechanics but I have trouble with bra-ket notation and operators…

Let’s say we have a photon moving along the cartesian z-axis. It is polarized and its state is

Psi(theta) = cos (theta) x1 + sin(theta) x1

Here, x1 and x2 are the base vectors.

The book states that a rotation about z axis is represented by an operator U, which has the matrix (respective to x1 and x2 base):

cos(fi) sin(fi)

-sin(fi) cos(fi)

It is the next step I have trouble with, the book states that by applying a rotation to psi(theta) you will get psi(theta+fi).

When I use simple matrix multiplication of U and psi, I don’t get this result but rather Psi(fi-theta)…

I did manage to produce the correct result when I used hermetian conjugate od U… Why is this so?

## Homework Equations

What is the correct procedure and why? What am I doing wrong?

## The Attempt at a Solution

Simple matrix multiplication...