# 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

thanks in advance

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?

Also, please type out your expressions instead of attaching them as images.

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.

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