## Homework 9

1. An electron in the Hydrogen potential is in the state . Find the value of that properly normalizes the state. What is the probability that the electron be found in the ground state of Hydrogen?

2. An electron is in the state of hydrogen. Find its wave function in momentum space.

3. A spin particle is in an eigenstate of with eigenvalue at time . At that time it is placed in a constant magnetic field in the direction. The spin is allowed to precess for a time . At that instant, the magnetic field is very quickly switched to the direction. After another time interval , a measurement of the component of the spin is made. What is the probability that the value will be found?

4. Consider a system of spin . What are the eigenstates and eigenvalues of the operator ? 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 subsequent measurement of yields ?

5. Let's define the u axis to be in the x-z plane, between the positive x and z axes and at an angle of 30 degrees to the x axis. Given an unpolarized spin beam of intensity going into the following Stern-Gerlach apparati, what intensity comes out?

Jim Branson 2013-04-22