Study Guide for final in Chem 442 Spring 2000

 

This will be a comprehensive exam.

Below are the high points basically taken in order of lectures.

 

  1. Give two examples of the failures of Classical mechanics and explain how a Quantum mechanical description remedied the problem.
  2. Know the form of the radiation distribution from a Black-body radiator at various temperatures.
  3. Classical definition of angular momenta.
  4. Be able to give time independent and time dependent Schrodinger equatu equations and identify all terms.
  5. What is the difference between the "wave packet" solution for a free particle motion and the normal, simpler, solution?
  6. Be able to make a plot for the transmission probability versus in coming energy of a particle going through a barrier.
  7. What ate the solutions for a particle in a box? (General form-no need to know the normalization constant)
  8. What is the advantage of using a "centro-symmetric" coordinate system ?
  9. Do the operators for linear momentum and position commute?
  10. Hooke’s law.
  11. Force constant is related to the sq. root of the vibrational frequency.
  12. Hermite polynomials are the solutions to the harmonic osc. Schrodinger equation.
  13. Be able to make a plot of the vibrational wave functions for v=0, 1 and 2.
  14. What is the non-classical region for the harmonic osc ?
  15. What is the Born interpretation of the wave function and why does that led to quantization of the vibrational wavefunctions?
  16. What does "orthonormal" mean?
  17. How is the "average value" determined in Quantum Mechanics?
  18. What is the "correspondence principle"? What does it imply about the shape of the wavefunction for the harmonic oscillator as the quantum numbers get large?
  19. Which of the orbital angular momentum operators commute?
  20. If two operators commute what does that imply about the product of the variance of the physical properties that these operators describe?
  21. What is the q.M. definition of varience?
  22. Know that the spherical harmonics are the eigenfunctions of the orbital angular momentum operators. What are the eigenvalues of L2 and Lz operators.
  23. Know that the spherical harmonic depend only upon two coordinates.
  24. Definition of a reduced mass for a two particle system. What is the advantage of using it.
  25. The radial functions distribution function is always real.
  26. In an electron in a 3d orbital further or closer to the nucleus than an electron in a 3p orbital?
  27. Does the H-atom energies depend upon the l quantum number?
  28. Why so electrons in "s-orbitals" exhibit Fermi contact interaction and electrons in other type of orbitals do not?
  29. Are electrons Fermions? What type of particles are bosons?
  30. What is the order of magnitude for the spin-orbit interaction in H-atom versus Fe-atom?
  31. Roughly how big is the earth’s magnetic field? How big is the field in an ESR spectrometer? How much is the splitting between the spin up and spin down states of an electron in the earth’s magnetic field?
  32. Know how to derive the Clebcsh-Gordon series for the sum of two angular momenta. Be able to make a vector model to illustrate the series.
  33. Know how to use a Table of Clebcsh-Gordon coefficients. I will ask for the wavefunction for j= 3/2 arising from s=1/2 and I=1.
  34. Hund’s rules.
  35. Know how to derive the term symbols arising from a simple configuration.
  36. Why is perturbation treatment so useful in solving "real life" quantum problems?
  37. First order energy correction for a perturbed particle in a box.
  38. Show that the first order energy correction to the for the Stark effect of a linear molecule =0.
  39. Variation principle. I will give trial function for a particle in a box and you will use the solve for the energy like homework.
  40. What is "central field approximation?
  41. What is the procedure for performing a Roothaan Hartree Fock calculation?
  42. Why so we write the electronic wavefunctions as Slater determinants?
  43. Be able to use degenerate perturbation theory for a simple problem. For example we may consider the proton/electron interaction in the ground state of H-atom. The interaction Hamiltonian is = I*S (=-I1S-1+ I0S0-I-1S1) where we have used the spherical operator form. (see lecture #30).
  44. Problems 8-1, *-2 amd *-3 from Atkins &Friedman (Handout on last day of class).