Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wave function question

  1. Oct 24, 2012 #1
    http://books.google.rs/books?id=vrc...=0CB0Q6AEwAA#v=onepage&q=nolting RKKY&f=false

    Here in the page 203 is defined ##|\vec{k}_i^{(i)},m_{s_i}^{(i)}\rangle## and also ##|0,f\rangle=|0\rangle|f\rangle##
    what that notation means?
    What is ##|0,f\rangle=|0\rangle|f\rangle##?
    If operator ##\hat{c}_{\vec{k},\sigma}^+## creates electron with wave vector ##\vec{k}## and spin ##\sigma##.
    What is
    [tex]\hat{c}_{\vec{k},\sigma}^+|0,f\rangle[/tex]?
     
  2. jcsd
  3. Oct 24, 2012 #2

    ZapperZ

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    This is not clear. Are you asking what a bra-ket notation mean, or are you specifically asking what a state |a>|b> mean?

    Zz.
     
  4. Oct 24, 2012 #3
    Only in this case. How operator ##\hat{c}## attacks ##|0,f\rangle##?
     
  5. Oct 24, 2012 #4
    For example
    [tex]\langle 0;f|\hat{C}_{i\sigma}^+|0;f\rangle=?[/tex]
     
  6. Oct 24, 2012 #5

    Matterwave

    User Avatar
    Science Advisor
    Gold Member

    You have to define the state the the operator...these are defined things...
     
  7. Oct 25, 2012 #6
    I think it is just for two separate things so it can be written as product.Any operator associated with electron will act on second one not on first one
     
  8. Oct 25, 2012 #7
    Well I can give more information. But I gave in first post book and the page. But ok...
    [tex]\hat{s}_i^z=\frac{\hbar}{2}(\hat{c}_{i\uparrow}^+ \hat{c}_{i\uparrow}-\hat{c}_{i\downarrow}^+\hat{c}_{i\downarrow})[/tex]
    [tex]\hat{s}_i^+=\hbar \hat{c}_{i\uparrow}^+ \hat{c}_{i\downarrow}[/tex]
    [tex]\hat{s}_i^-=\hbar \hat{c}_{i\downarrow}^+ \hat{c}_{i\uparrow}[/tex]

    In text.
    ''Without perturbation electron exist in their unpolarised ground state. In addition since they don't interact with each other, the unperturbed electron ground state can be written as the antisymetrised product of single electron states
    [tex]|\vec{k}_i^{(i)},m_{s_i}^{(i)}\rangle=|\vec{k}_i^{(i)}\rangle |m_{s_i}^{(i)}\rangle[/tex]
    where the spin magnetic quantum number ##m_{s_i}^{(i)}## takes the values ##\pm \frac{1}{2}##. ##|\vec{k}_i^{(i)}\rangle## is wave vector where superscript refers to the particle number. Furter since we want to treat conduction electrons as s electrons, which excludes spin orbit interraction, we can separate the spin and the space parts. Let
    [tex]|0;f\rangle=|0\rangle|f\rangle[/tex]
    ''
    Can you now give me explanation. What is ##|0\rangle##? What is ##|f\rangle##? And how defined operators act on this state? Tnx.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Wave function question
Loading...