Eric R. Bittner

Pursuing a graduate degree in theoretical chemistry requires considerable amounts of hard-work, talent, focus, and dedication. It is perhaps the most difficult subdiscipline of chemistry to work in since the field is rich with hard-working and talented individuals competing for small number of jobs and resources. Theory students must not only have an excellent grasp of Physical Chemistry, but must also posess highly developed mathematical and computational skills. I requre all my students to take at least one advanced course in physics and take a course in Mathematical Physics before taking their oral progress examination. In addition to scoring well on the Physical Chemistry Diagnostic Exam, I require all students that are interested in my group to complete a brief examination prior to being accepted as a student in my group.

Bittner Group Entry Exam 07

The following set of problems will help me evaluate your preparation and ability to do research in my group. Please submit your answers electronically to Prof. Bittner (email: bittner@uh.edu ).
I will accept submissions up until 15-Jan-2008.

1. 1. Prove the following identity:
      
   2. Discuss the significance of this expression.
2. An electron is trapped in a spherical cavity of a deformable medium (such as water) with a radius r_e. Assuming the trapping potential is of the form:
   
   1. What is the radius of the cavity if the energy difference, , between the two lowest energy states is 1.75eV?
   2. What is pressure exerted by the trapped electron on the medium when the electron is in the ground state?
   3. Using the reversible work theorem, dW = -P dV, calculate the work required to compress an electron in the lowest energy state until .
3. Evaluate the integral
   
   where n is a positive integer.
4. 1. Determine the spectral density of a damped harmonic oscillator driven by a random noise source R(t)
      
      with
      
      and
      .
   2. What is ?
   3. What is the significance of the relation between the damping constant and the fluctuations of the noise source?
   4. How would your expression be modified if the system were to be quantized.
5. Use the Born-Sommerfield quantization rule to calculate the allowed energy levels of a ball of mass m bouncing elastically in the vertical direction.
6. Write a 4-5 page review (+ references) of one or two paper(s) published by my group within the last year that you find interesting. A complete listing of our publications can be found at k2.chem.uh.edu/cgi-bin/bib.cgi