- #1
max_jammer
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Hello all,
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?
What is the correct procedure and why? What am I doing wrong?
Simple matrix multiplication...
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...