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.
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.
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?