- #1
alizeid
- 14
- 0
Poster has been reminded (again!) to use the Template when starting schoolwork threads.
Why is the expectation value of the commutator not zero in method 1?
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Homework Help Overview
The discussion revolves around the expectation value of the commutator in quantum mechanics, specifically in the context of polarized photons represented in different bases. The original poster attempts to understand discrepancies in their calculations using two methods to extract the expected value of a |+45> polarized photon in the HV basis.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- Participants question the origin of a minus sign in the calculations and the nature of the operators involved. There is also a focus on the definition of the |45> state and its relation to the HV basis, with some participants expressing confusion over the expectation value of the commutator being zero.
Discussion Status
The discussion is active, with participants providing guidance on the need for clarity regarding the definitions used in the problem. Some participants assert that the expectation value of the commutator should not be zero, while others argue that it must be zero for the given state, indicating a divergence in interpretations.
Contextual Notes
There is a lack of information regarding the textbook being referenced, which is noted as crucial for understanding the problem. Additionally, the distinction between states and operators is under discussion, which may affect the interpretation of the problem.
- #2
- 22,827
- 14,867
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.
Also, please type out your expressions instead of attaching them as images.
- #3
alizeid
- 14
- 0
why are they different operators? according to the book, they are the sameOrodruin said:
- #4
- 22,827
- 14,867
Then you either copied the book wrong or the book is wrong.
- #5
- #6
- 22,827
- 14,867
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.alizeid said:
- #7
- #8
- 22,827
- 14,867
So what is the problem?
- #9
alizeid
- 14
- 0
Orodruin said:
The expectation value of the commutator should NOT be zero. the commutator do not commut therefore the answer is wrong
- #10
- 22,827
- 14,867
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.alizeid said:
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