19.9 Homework
- An electron in the Hydrogen potentialV(r) =−e
2
r is in the stateψ(~r) =Ce−αr. Find the
value ofCthat properly normalizes the state. What is the probability that theelectron be
found in the ground state of Hydrogen?- An electron is in theψ 210 state of hydrogen. Find its wave function in momentum space.
- A spin^12 particle is in an eigenstate ofSywith eigenvalue + ̄h 2 at timet= 0. At that time it is
placed in a constant magnetic fieldBin thezdirection. The spin is allowed to precess for a
timeT. At that instant, the magnetic field is very quickly switched to thexdirection. After
another time intervalT, a measurement of theycomponent of the spin is made. What is the
probability that the value− ̄h 2 will be found? - Consider a system of spin^12. What are the eigenstates and eigenvalues of the operatorSx+Sy?
Suppose a measurement of this quantity is made, and the system is found to be in the eigenstate
with the larger eigenvalue. What is the probability that a subsequentmeasurement ofSyyields
̄h
2? - Let’s define the u axis to be in the x-z plane, between the positive xand z axes and at an
angle of 30 degrees to the x axis. Given an unpolarized spin^12 beam of intensityIgoing into
the following Stern-Gerlach apparati, what intensity comes out?
I→
{
+
−|
}
z→
{
+
−|
}
x→?
I→
{
+
−|
}
z→
{
+|
−
}
u→?
I→
{
+
−|
}
z→
{
+|
−
}
u→
{
+|
−
}
z→?
I→
{
+
−|
}
z→
{
+
−
}
u→
{
+|
−
}
z→?
I→
{
+
−|
}
z→
{
+|
−
}
u→
{
+|
−
}
x