be, sfmw defecfer A
dkecfev T
T ale-rector B infer fevencv.
oyens m shv
(0 gum-0 M13 N
Photon! +03%
rmgh.
Resudts : Only ddectcv A W B 34 sigma/S
9 Pavde behavior (g! [541+ .
If 'Hu beam 5on Haroyk defecter A and B an
Ywmblncd ,
infareran is observed .
Some Useful Facts for the Physics 115A Midterm
Probabilities:
b
a
Prob(a < x < b at time t) =
Probability current:
t ( )
Expectation values:
O(x, p) =
Uncertainties:
x2 x
x =
2 1/2
x
x
h
2im
with J(x) =
(x, t)O(x, h x )(x, t)dx
i
,
p2 p
p =
2 1/2
i (
Some Practice with Linear Algebra
Here are some exercises to practice some of the linear algebra used in quantum mechanics. These are
not required, and are not for creditdont turn in answers, though you can ask if you have questions.
1. Adjoints
The gener
Some Useful Facts for Physics 115A
Hilbert spaces: states | ; complex linear a| + b| is also a state principle of superposition
inner product | = | ; |c = c | and c| = c |
orthonormality: ei |ej = ij
completeness: | =
ei | |ei for any |
i |ei ei | = 1
fo