This page will not have complete notes, but it will have at least a lecture schedule.

Date	Topic
May 1	We finished the fine structure correction for the hydrogen atom. We looked at the Zeeman effect (weak, strong and intermediate field). This included working part of problem 6.23.
April 26	We completed the example in the text on degenerate perturbation theory and worked problem 6.9. We began to determine the relativistic correction to the energies for the hydrogen atom.
April 24	We determined the first order correction to the wavefunction and the second order correction to the energy. We examined degenerate perturbation theory. Some hints for the homework problems will be here shortly.
April 19	We discussed the second exam. We began talking about nondegenerate perturbation theory and determined the first order correction to the energy. We worked problems 6.1 and 6.2.
April 17	We looked at the physical significance of the constants a and b that appear in the distribution functions for distinguishable particles and for particles that obey Bose-Einstein and Fermi-Dirac statistics. We worked as examples problems 5.25 & 5.26. We applied the Bose-Einstein distribution function to a system of non-interacting bosons (photons in a cavity) and worked problem 5.27 which is a derivation of Wien's Law and as promised, here is problem 5.28.
April 12	Test Day
April 10	We completed our look at the "Dirac comb model for the potential and looked at potential values for the energies and the bands and gaps that result from this model. We began to look at quantum statistical mechanics. Six particles with total energy 8E
April 5	We looked at the free electron model for electrons in a solid and found the "degeneracy pressure". We worked problem 5.31 and briefly discussed 5.32 (solution available in HW). We looked at a more realistic potential, the Dirac comb.
April 3	We showed that the expectation value of the separation between particles is different for bosons, fermion, and distinguishable particles. We looked at the Hamiltonian for more complex atoms and solved it for helium given the very significant assumption that the electrons do not interact. We worked problem 5.10 (part 1) & (part 2) and which gave us a correction to the estimate of the ground state energy we had made.
Mar 29	We began to look at a system of two identical particles and examined the difference between fermions and bosons. We discussed symmetric and anti-symmetric wave functions and the parity operator. We worked problems 5.2 a&b, 5.3 and 5.4a.. The rest of 5.2 and 5.4 are in the HW solutions.
Mar 27	We discussed some of the pending homework problems. We worked problem 4.35 which looked at the singlet and triplet states for two spin 1/2 particles. We then determined the coefficients for constructing a state with j = 1, m = 1 from two states with j1 = 2 and j2 = 1 and looked at how to get those same coefficients from the tables, problem 4.37.
Mar 22	We determined the expectation values for the various components of the spin angular momentum. We looked at representing the spin state as a linear combination of the eigenfunctions of either Sz or Sx. We looked at an electron in a magnetic field and determined the frequency of the Larmor precession and explained the results of the Stern-Gerlach experiment. Table of Clebsch-Gordan coefficients
Mar 20	We found the eigenfunctions for L2 and Lz, which turned out to be the spherical harmonics. No surprise there. We worked problem 4.19. We looked at how the inner product notation and the orthogonality of the wave functions simplifies the calculations <Y |Li|Y>. We then introduced the idea of intrinsic angular momentum or spin. Using the matrix notation, we found the eigenfunctions for S2 and Sz, and the matrix representation for those operators along with Sx and Sy.
Mar 15	We determined the first excited states for the hydrogen atom. Next, we looked at the form for the angular momentum operator and derived the commutation relations for those operators. We derived the form of the raising and lowering operators. We recognized that there must be an upper state that if we try and raise that state we obtain zero and a lower state that returns zero if the lowering operator acts on it. This gave us mT = -mB = l (that is "el" not one) and that l= (l+1)l. We found the x, y, z components of the angular momentum operator in terms of spherical coordinates.
Mar 13	We discussed the solutions to exam 1. We worked problem 4.9 which is the finite spherical well for l = 0. We solved the Schrodinger equation for the hydrogen atom, or at least have a solution to the differential equation. We saw that the solution we have now is not a good solution from a physical standpoint. We saw that the solution to the problem that our solution goes to infinity was to truncate the power series. This truncation leads to energy quantization and leads to the results Bohr obtained for the hydrogen atom.
Mar 1	Recognizing that many of the potentials we will encounter have spherical symmetry, we recast the Schrodinger equation into spherical coordinates and looked at the solutions to the angular portion of the wave function. We looked at the problem of the infinite spherical well.
Feb 27	We rephrased the fundamental ideas of quantum mechanics in terms of the ideas developed in the linear algebra section. We discussed the properties of operators associated with observable quantities. We derived the uncertainty principle based on the commutator of two operators and rederived the uncertainty principle for position and momentum. We began quantum mechanics in three dimensions and worked the problem of the bound states for a 3-d infinite well in the shape of a cube.
Feb 22	Test Day
Feb 17	We introduced the idea of a function space, defined the inner product for such a space and worked problem 3.26.
Feb 15	We finished working problem 3.9. We reviewed how the elements of a matrix depend on the choice of basis and worked problem 3.14. Next, we showed how to determine the eigenvectors and eigenvalues for a tranformation.
Feb 13	We worked problems 3.4 (using the Gram-Schmidt procedure to generate an orthonormal basis from one that is not orthonormal) and 3.5 (proof of the Schwartz inequality). We looked at linear transformations as matrices and defined several properties of matrices. We looked at how the elements of a matrix depend on the choice of basis.
Feb 09	We looked at the scattering states for the finite square well and determined the transmission coefficient by applying the boundary conditions. I'll try to post that derivation. We began a review of linear algebra to help us develop a formalism for quantum mechanics.
Feb 07	We worked problem 2.26., which was a double delta-function potential. We examined the bound states of the square well and determined the number of bound states and the energies of those states for a variety of potential strength parameters.
Feb 01	We demonstrated that for a free particle the group velocity rather than the phase velocity agrees with our classical prediction for the velocity. We defined the dirac delta function and found the bound states and the scattering states for a delta function potential well and the scattering states for a delta function barrier.
Jan 29	We continued our discussion of the harmonic oscillator by showing that the only way to have physically acceptable solutions is to truncate our power series solution. This condition leads to quantization of energy and the energies En = (n+1/2)(h/(2p))w. We worked problem 11 from Chapter 2 which gives useful information for HW prob 12 and worked problem 16 which asked us to determine the coefficients for the fifth and sixth order Hermite polynomials. Next we discussed methods of dealing with the "problems" we encounter with the traditional free particle wave function.
Jan 25	We discussed the simple harmonic oscillator and found solutions to the Schrodinger equation with that potential using the method of raising and lowering operators. Next, we began to solve the Schrodinger equation for the harmonic oscillator using the analytic method. Extra Information Prob 2.11 Prob 2.13
Jan 23	We worked through the remainder of problem 6 from Chapter 2, verified the theorems in problem 1 of Chapter 2 and worked problem 9 from Chapter 2, which asked us to determine the expansion cofficients for the function defined in problem 8.
Jan 18	We verified in extreme detail the fact that once the wave function is normalized, it remains normalized. We also determined the time derivative of the expectation value of the position and used that to define the momentum operator. We also introduced (briefly) the uncertainty principle. Next we found the time independent Schrodinger equation and discussed the properties of the solutions to this equation. We found the solutions to the Schrodinger equation for a particle in an infinite well.
Jan 16	We reviewed line spectra and the Bohr atom. We discussed the wave nature of particles and gave an argument (though not rigourous proof) for the Schrodinger Equation. We discussed probability and worked problems 1 & 3 from Chapter 1. We discussed the normalization condition and showed that it is time independent.
Jan 11	Introduction