I 3 =
3
4
I 2 =
1
16
I 0
Now lets see what happens if we remove the blocking in apparatus 2.
Oven(I 0 )→
+
0 |
−|
z(I 1 )→
+
0
−
x(I 2 )→
+|
0
−
z(I 3 )→
Assuming there are no bright lights in apparatus 2, the beam splits into 3 parts then recombines
yielding the same state as was coming in,ψ+(z). The intensity coming out of apparatus 2 isI 2 =I 1.
Now with the pure stateψ(+z)going into apparatus 3 and the top beam being blocked there, no
particles come out of apparatus 3.
I 3 = 0
By removing the blocking in apparatus 2, the intensity droppedfrom 161 I 0 to zero. How
could this happen?
What would happen if there were bright lights in apparatus 2?
18.10.8Time Development of anℓ= 1 System in a B-field: Version I
We wish to determine how an angular momentum 1 state develops with time (See Section 7.4),
develops with time, in an applied B field. In particular, if an atom is in the state with x component
of angular momentum equal to + ̄h,ψ(+x), what is the state at a later timet? What is the expected
value ofLxas a function of time?
We will choose the z axis so that the B field is in the z direction. Then we know the energy eigenstates
are the eigenstates ofLzand are the basis states for our vector representation of the wave function.
Assume that we start with a general state which is known att= 0.
ψ(t= 0) =
ψ+
ψ 0
ψ−
.
But we know how each of the energy eigenfunctions develops with time so its easy to write
ψ(t) =
ψ+e−iE+t/h ̄
ψ 0 e−iE^0 t/ ̄h
ψ−e−iE−t/ ̄h
=
ψ+e−iμBBt/ ̄h
ψ 0
ψ−eiμBBt/ ̄h
.
As a concrete example, let’s assume we start out in the eigenstate ofLxwith eigenvalue + ̄h.
ψ(t= 0) = ψx+=
1(^21)
√
2
1
2
ψ(t) = ψx+=
e−iμBBt/h ̄(^21)
√
2
eiμBBt/ ̄h
2