# Homework Help: Exception value in QM

1. Jan 2, 2018

### alizeid

• Poster has been reminded (again!) to use the Template when starting schoolwork threads.
I'm trying to extract the expected value of a |+45> polarized photon in the HV- base. I do it in two ways, one is correct and the other I get wrong answer. What am I doing wrong in the first method that is wrong?

method 1

method 2

2. Jan 2, 2018

### Orodruin

Staff Emeritus
You computed the expectation value of different operators. Where did the minus sign come from in your second method?

3. Jan 2, 2018

### alizeid

why are they different operators? according to the book, they are the same

4. Jan 2, 2018

### Orodruin

Staff Emeritus
Then you either copied the book wrong or the book is wrong.

5. Jan 2, 2018

### alizeid

The real problem is

I get the expectation value of the commutator to zero, even for operator | 45>. This can not be correct. I can not solve this problem, can you help me?

6. Jan 2, 2018

### Orodruin

Staff Emeritus
The problem formulation is of little use unless you define the $|45\rangle$ basis in terms of the HV one and define what is meant by $\mathcal P_{HV}$. Since you have not told us what textbook you are using and we most likely will not have direct access to it, this is crucial information.
$|45\rangle$ is a state, not an operator.

7. Jan 2, 2018

8. Jan 2, 2018

### Orodruin

Staff Emeritus
So what is the problem?

9. Jan 2, 2018

### alizeid

The expectation value of the commutator should NOT be zero. the commutator do not commut therefore the answer is wrong

10. Jan 2, 2018

### Orodruin

Staff Emeritus
No it isn’t. In fact, the expectation of the commutator must be zero for the given state! Anything else would violate the uncertainty relation.