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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- March 1st 2009, 06:02 PMthehollow89Initial 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. - March 1st 2009, 11:46 PMCaptainBlack
- March 2nd 2009, 03:44 AMthehollow89
- March 2nd 2009, 05:58 AMHallsofIvy
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. - March 3rd 2009, 04:17 PMmatt12321
how would i calculate another state vector from this?

like S2? - March 3rd 2009, 04:19 PMthehollow89
- March 3rd 2009, 04:21 PMmatt12321
- March 3rd 2009, 04:23 PMthehollow89
- March 3rd 2009, 04:44 PMmatt12321
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.. - March 3rd 2009, 04:45 PMthehollow89
Alright cool.

- March 3rd 2009, 05:51 PMmatt12321
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? - March 5th 2009, 01:30 PMa_n
i go to mcmaster too...im just wondering how to do question 6 because i really dont understand what its asking