[題目] 量子力學 time-dependent perturbation
[領域] 量子力學 (題目相關領域)
[來源] 考古題 (課本習題、考古題、參考書...)
[題目]
Solve the gyromagneyic ratio of spin for the particle be g. Suppose we turn
off the harmonic potential and place this particle in a 3D uniform magnetic
field B=(exp(-t/t0), 0, 1-exp(-t/t0)), where t is time and to is a postive
time constant. The magnetic field is turned off for t>0 and we assume that
the orbital motion can be neglected. If at t=-無限, this particle is in the
spin up state |+> (Here z-axis is the quantization axis and |-> denotes the
spin down state), be treating this problem as a time-dependent perturbation
problem, to the order of O(B), find the probability for finding the particle
in the state |-> at t=0.
[瓶頸] (寫寫自己的想法，方便大家為你解答)
這題我看到的解答寫了一半,用
|1-exp(-t/t0) exp(-t/t0)| |1 0| |-1 1|
H=eg(S．B)/2mc=egh/(8mc．pi)| |=A| |+A| |exp(-t/t0)
|exp(-t/t0) exp(-t/t0)-1| |0 -1| |1 1|
=H0+V
|-1 1|
=> V=A| |exp(-t/t0), where A=egh/4mc
|1 1|
i(h/2pi)*(dCn/dt)= Sigma {Vnm*exp[-i(En-Em)t/(h/2pi)]}
算出 dC1/dt, dC2/dt和 C1, C2關聯的矩陣
| dC1/dt | | -1 exp(iw_12t)| | C1 |
i(h/2pi)| |=A| |*exp(-t/t0)*| |
| dC2/dt | | exp(-iw_12t) 1| | C2 |
, where A=egh/4mc, w_12= 2pi*(E1-E2)/h
| -1 exp(iw_12t)|
然後算 | |的eigenvalues,和eigenvectors.
| exp(-iw_12t) 1|
但我不是很懂,且最後也沒有解出答案
謝謝大家看完我打的那些數學算式,煩請高手指點一下,感謝!
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