- #1
FatPhysicsBoy
- 62
- 0
Homework Statement
Homework Equations
N/A
The Attempt at a Solution
I am having trouble getting my head around these questions, the first part a) wasn't too tricky, I used the fact that eigenfunctions of a Hermitian operator [itex]\hat{O}[/itex] are orthogonal and got my normalisation constant = 1/14.
However, I'm having trouble understanding what part b) c) and d) are talking about, here's my understanding:
b) So, I have three eigenfunction equations involving [itex]\hat{O}[/itex]: [itex]\hat{O} \phi_{1}(x) = \phi_{1}(x)[/itex], [itex]\hat{O} \phi_{2}(x) = 5\phi_{2}(x)[/itex], and [itex]\hat{O} \phi_{3}(x) = 9\phi_{3}(x)[/itex] but what does it mean by physical quantity corresponding to [itex]\hat{O}[/itex] in the state [itex]\phi (x)[/itex]? Does it mean the eigenvalues of each equation? If so, would the 'possible' results just be 1, 5, & 9? If so, why? Then how do I go about calculating the probability of each outcome? I am very confused!
c) Now, I understand that [itex]<\hat{O}> = \int_{-∞}^{∞} \psi^{*}(x) \hat{O} \psi (x)[/itex] but I don't understand how this will lead to what the question is asking for..
d) I just don't understand this.
Basically, I'm having trouble understanding the questions, what they mean, and what they're asking me to do! Any help would be much appreciated!
Thank you
Attachments
Last edited by a moderator: