1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 2nd year university Quatum Physics paper. Please help.

  1. Aug 10, 2009 #1
    Hello there. I am a 2nd year uni student studying chemistry. I have a paper in a few weeks on the foundations of physical chemistry.
    I am having a problem with some quetions and would appreciate any help. Thank you to any who help.

    1.Can the expectation value of the rotational angular momentum of a diatomic molecule
    be used to predict what value will be obtained experimentally if the rotational angular
    momentum of a single molecule is measure only once? Justify.

    My answer:

    The measurement of the observable <L> must be an eigenvalue to L(operator).

    L(operator)fn(x)=Lnfn(x) n=1,2,3...

    If the system is in an eigenstate of L(operator), the result gained must be of the observable L, that can only be of the particular eigenvalue characteristic of that eigenstate:

    say Ψ(x)=f7(x)
    then L=L7

    Whereas if the system is not an eigenstate of L, the result of one measurement of a single diatomic can be in any one eigenstate of L(operator) but will be completely unpredictable:


    The eigenvalue is therefore completely unpredictable.

    The expectation value <L> would be given by:
    Integration over all space of the wavefunction(in all co-ordinates)*L(operator) d(all co-ordinates).

    Therefore <L> and the single measurement are unlikely to be the same.
  2. jcsd
  3. Aug 10, 2009 #2
    Your answer is essentially correct, though you may not have a full handle on the topic.

    The expectation value is the average value you would expect to obtain if you made the measurement billions of times. A simple example system is one in which you have a linear combination of a spin up and spin down particle wave function

    [tex]\psi = \frac{1}{\sqrt{2}}\big(\,\mid\uparrow\rangle + \mid\downarrow\rangle\,\big)[/tex]

    If you make just ONE measurement of the spin you will get either +1/2 or -1/2. But if you make a LOT of measurements and average them, you will get closer and closer to zero, which is also the expectation value.
  4. Aug 10, 2009 #3
    Thank you. Can anyone else help a bit more? Using the above question?
  5. Aug 11, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Look at it this way: The expectation value of rolling a standard die is 3.5. Can you use this to predict what you will get before you roll it?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook