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Math Help - Initial state vector

  1. #1
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    Initial state vector

    Express our initial state vector S0 as a linear combination of our eigenvectors. The initial state vector is:
    _
    |0|
    |1|
    |0|
    ---
    This material isn't in my textbook. Any help? I appreciate all the help I've received. Just sharing. This forum rocks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thehollow89 View Post
    Express our initial state vector S0 as a linear combination of our eigenvectors. The initial state vector is:
    _
    |0|
    |1|
    |0|
    ---
    This material isn't in my textbook. Any help? I appreciate all the help I've received. Just sharing. This forum rocks.
    Please provide more information, like what are your eigen vectors, or what matrix (or whatever) are they the eigen vectors of.

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Please provide more information, like what are your eigen vectors, or what matrix (or whatever) are they the eigen vectors of.

    CB
    Oh Sorry I didn't know how much info was needed for this part of the question. The eigenvectors are:

    ----
    0
    t ,
    -t

    ----

    ,

    --------
    t
    -5/2t
    -4/9t
    -------

    and

    ------
    t
    1/2t
    2/5t
    ------
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  4. #4
    MHF Contributor

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    You eigenvectors depend on t but your initial state vector doesn't? That's impossible. I suspect that you mean the eigenvectors are <0, 1, -1>, <1, -5/2, -4/9>, and <1, 1/2, 2/5>.

    If so, then you need to find numbers a, b, c so that
    a<0, 1, -1>+ b<1, -5/2, -4/9>+ c<1, 1/2, 2/5>= <0, 1, 0>

    That is the same as saying <b+ c, a-(5/2)b+ (1/2)c, -a- (4/9)b+ (2/5)c>= < 0, 1, 0> or b+ c= 0, a- (5/2)b+ (1/2)c= 1, -a+ (5/9)b+ (2/5)c= 0. Solve those equations for a, b, c.
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  5. #5
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    how would i calculate another state vector from this?
    like S2?
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  6. #6
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    Quote Originally Posted by matt12321 View Post
    how would i calculate another state vector from this?
    like S2?
    I take it you go to Mcmaster too? I'm trying to figure it out.
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  7. #7
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    Quote Originally Posted by thehollow89 View Post
    I take it you go to Mcmaster too? I'm trying to figure it out.
    ya,
    this assignment is going to take me forever...
    well actually, theres only three more real questions after this one.
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  8. #8
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    Quote Originally Posted by matt12321 View Post
    ya,
    this assignment is going to take me forever...
    well actually, theres only three more real questions after this one.
    Yeah, are you using maple or online matrix multipliers? I'll be going to the help center tomorrow around 5:30-8:30 tomorrow if you wanna...well...cheat lol. Mclean doesn't even care if we cheat lol.
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  9. #9
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    i'm using online multipliers...
    i used this other site to calculate the eigenvalues/vectors
    but i did it by hand aswell..

    i might be there tomorrow, but i'm not sure..
    i'm supposed to be going somewhere tomorrow evening..
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  10. #10
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    Alright cool.
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  11. #11
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    well i'm almost done now... i think i've done all i can do without more help...
    have you done #7?
    seems really dumb to me..
    i haven't done the second part of number three...
    and can't finish 9 because i don't have the final answer for 5 (the one above)
    have you figured any of these out?
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  12. #12
    a_n
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    i go to mcmaster too...im just wondering how to do question 6 because i really dont understand what its asking
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