mirror of
https://asciireactor.com/otho/phy-521.git
synced 2024-12-04 18:45:07 +00:00
22 lines
434 B
Groff
22 lines
434 B
Groff
|
3.8
|
||
|
|
|
||
|
|
a)
|
||
|
|
|
||
|
|
check that the eigenvalues of the hermitian operator in example 3.1 are real. show that the eigenfunctions are orthogonal.
|
||
|
|
|
||
|
|
Qf = if'
|
||
|
|
|
||
|
|
the eigenvalues are 0,+- 1, etc., which are obviously real.
|
||
|
|
|
||
|
|
|
||
|
|
pick two arbitrary eigenfunctions:
|
||
|
|
|
||
|
|
f = A exp(-i q phi)
|
||
|
|
g = A exp(-i q' phi)
|
||
|
|
|
||
|
|
<f|g> = A*A int[exp(i q phi) exp(-i q' phi)] dphi[0,2pi]
|
||
|
|
= A*A int[exp(i (q - q') phi)] dphi[0,2pi]
|
||
|
|
= A*A [i(q-q')]^-1 [exp(i(q-q') phi)]|[0,2pi]
|
||
|
|
|
||
|
|
|