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Week of Dec 2
Readings: Your textbook covers some of this material very briefly in Chapter 1.4. However, you should be able to find easily a more detailed treatment of waves almost any introductory calculus-based physics textbook. For instance, see Tipler & Mosca, 5th edition, Chapters 14 and 15.
After preliminary administrative info, this lecture will cover briefly some key points about wave phenomena that should have been covered in prerequisite physics courses (simple harmonic motion, traveling and standing wave solutions to the wave equation). You should make sure you're comfortable with this material in order to enjoy the rest of the course.
Readings: Your textbook only briefly covers this material in 1.4 and 1.8, but again, you should be able to find easily a treatment in almost any introductory physics textbook. For instance, you will be able to find discussion of interference in Tipler & Mosca, 5th edition, 33.1-33.3.
We will do a bit more review of wave properties: we'll very briefly go over transverse vs. longitudinal waves, energy in waves, and reflections. We'll discuss constructive and destructive interference generally, and do a brief review of electromagnetic waves. Then we'll look at interference of electromagnetic waves via discussion of Young's double slit experiment.
Readings: Again, this material is covered in freshman physics texts. For example, see Tipler and Mosca 33.3-33.5, 33.8.
We will look more quantitatively at Young's double slit experiment. We'll talk about what happens if there are multiple slits, and I'll mention diffraction gratings. I will then introduce single slit diffraction.
Readings: Again, this material is in introductory physics texts.
We will finish discussion of the single slit diffraction pattern. The second topic will be an application of some of the ideas from the last few classes: interference in thin films.
Readings: BFG Ch 2-1 through 2-3 (although we will cover this material in a somewhat different order, and parts of this will be in later lectures).
We'll start by covering inertial reference frames and Newtonian relativity. We will then discuss the Michelson-Morley experiment, and how its shocking result can be explained by Einstein's postulates of special relativity (which we'll see later have even more shocking consequences!)
Readings: BFG rest of Ch 2 (except 2-6 and a few subsections), 3-1
We will start to explore the bizarre consequences of Einstein's postulates: simultaneity, time dilation and length contraction.
Readings: BFG 2-2, 2-4, 2-6, 3-2
We will finish up the consequences of Einstein's postulates: we'll derive Lorentz transforms, and the formulae for relativistic addition of velocities. Finally, we'll cover relativistic Doppler shifts.
Readings: BFG rest of Ch 3: most important is 3-3
This lecture will introduce concepts of relativistic momentum, energy and mass. We'll define relativistic momentum in the context of conservation of momentum, then turn to relativistic energy and conservation of mass-energy.
Readings: BFG 3-3,3-4
In this lecture we'll see relativity in real-life action. I will make some comments about units, talk about binding energy, and give some fission and fusion examples.
Readings: BFG Part 2 intro blurb pp. 101-107, 4-1, 4-4
In this lecture we'll look at at the beginnings of understanding of the quantum nature of light, using a semi-historical approach: we'll cover blackbody radiation (and the Stefan-Boltzmann law), and discuss the various attempts to describe it: the Wien relation, the Rayleigh-Jeans classical calculation, and finally Planck's successful quantum description of the blackbody spectrum.
Readings: BFG 4-2, 4-3
We will look at more experimental evidence for the quantum nature of light: first, the photoelectric effect (explained by Einstein in 1905, for which he won the Nobel Prize), and Compton scattering. Halfway through I'll make a short digression to talk about photomultiplier tubes.
Readings: BFG 4-5,4-6,4-7
We'll reexamine the wave-like nature of light, by looking at Young's two-slit interference experiment, and touch upon some of the conceptual issues resulting from light being both a particle and a wave. Then I'll introduce the idea, due to de Broglie, that familiar matter particles are waves too, and look at some experimental evidence supporting this idea: diffraction of electrons from crystals.
Professor Oh, Physics Department Director of Undergraduate Studies, will be guest lecturer.
Readings: BFG 5-1, 5-2
We will first briefly discuss diffraction gratings, in order to appreciate the spectroscope demo. After observing some spectral lines, we will discuss Bohr's attempt to explain atomic spectra, with his picture of electrons in circular orbits around a nucleus, with quantized angular momenta.
Readings: BFG 6-1, 6-2
We will start to go beyond the Bohr atom towards a more comprehensive description, and start to explore wave mechanics. We'll define wavefunctions in the context of the probability interpretation due to Born, then introduce the Schrödinger equation, and discuss its meaning. Finally we'll cover the plane wave solution for a free particle.
Readings: BFG 6-3, 6-4, 6-5
We'll define expectation values and operators, and write an operator for momentum, and for energy (the Hamiltonian). Then we'll look at the case of a separable wavefunction, for which it's possible to separate time and space parts of the Schrödinger equation, and write the time-independent Schrödinger equation. We'll define eigenfunctions and eigenvalues, and write this as an eigenfunction equation. Finally, we'll start to look at the classic example of a "particle in a box".
We'll go over the particle-in-a-box example in some detail, and then I'll make some comments on the meaning of eigenfunctions and eigenvalues.
Readings: BFG 7-1, 7-2
We'll revisit plane waves, which are eigenfunctions of momentum and completely unlocalized. Then we'll discuss how to describe localized particles by building wave packets, which are superpositions of plane waves.
Readings: BFG 7-3 through 7-5 (7-6 is optional)
After defining uncertainties a bit more precisely, I will introduce the general Heisenberg position-momentum uncertainty relation and, without going into computational detail, briefly go over some examples for particular wave packets. Next, we will go over some of the physical consequences: we'll discuss the two-slit experiment, and the way in which the uncertainty principle enforces consistency in the particle-wave picture.
Readings: BFG 8-1, 8-2
We'll finish up one thing left over from last class: the energy-time uncertainty principle. We'll look at two applications: spectral line width, and the idea of "virtual particles". Then we will start a new topic: we'll start to look at a wider class of solutions to the Schrödinger equation. The first example will be the description of particles impinging on a repulsive potential. We'll consider how the quantum picture differs from the classical one.
Readings: BFG 8-3, 8-4
We'll calculate the probability of reflection and transmission from a potential barrier for a particle with E>V_0, and then look quantitatively at the case of E less than V_0, corresponding to the phenomenon of quantum tunneling.
Prof. Glenn Edwards will give a tour of DFELL. Please meet him in the DFELL conference room at 10:20. Here are instructions on how to get there from the Physics building, and here is a map (the magenta line corresponds to the instructions, but you can also go around the LSRC).
Readings: BFG 8-5
We'll talk about bound states for a negative potential well (V_0<0) (the "finite square well"), which exist as even and odd solutions.
Readings: BFG 8-4, 6-6, 9-1
I'll finish up from last time an example for which tunneling is a real life effect: the scanning tunneling microscope. Then we will start moving beyond "cartoon" potentials and start to treat real-world solutions to the Schrödinger equations. We'll review what a central potential is, and look at the problem of finding general solutions to the 3D Schrödinger equation for a central potential.
Readings: BFG 9-1, 9-2
We will start to find general solutions to the 3D Schrödinger equation for a central potential, by separation of variables. The angular part of the equation can be solved generally without knowing the specific V(r); the solutions to the angular part involve spherical harmonics. We'll then proceed to make the connection between the central force Schrödinger equation solutions, which last class we developed mathematically, and physical observables. I'll introduce angular momentum as a quantum mechanical operator, and show how the eigenfunctions of L^2 and L_z are the very same Y_lm's we saw last class; the eigenvalues are sharp values corresponding to the l and m quantum numbers.
Substitute lecturer: Prof. Chandrasekharan
Readings: BFG 9-3
After finishing up the angular momentum story started last class, you will look at a few properties of angular momentum peculiar to the quantum picture. Then you will go back to the radial equation put aside last time, and cover the solutions for the specific Coulomb V(r), the set of allowed energies, and degenerate states.
Readings: BFG 9-4, 9-5; also review 1-7 on magnetic moment
I'll finish up a few points about H atom radial wavefunctions, introduced last class. We will then review the connection between magnetic moments and angular momentum, and show how the 2l+1-fold degeneracy of the hydrogen atom's nth energy level can be lifted by applying a magnetic field: this is the Zeeman effect. We'll look at experimental evidence for the existence of the degenerate states: the Zeeman effect in atomic spectra, and the Stern-Gerlach experiment.
Readings: BFG 9-5
We'll discuss spin, an intrinsic angular momentum, and its consequences. We'll look at the anomalous Zeeman effect, an energy splitting in an external magnetic field due to spin. Then we'll cover addition of angular momenta, which in quantum mechanics does not work the same way as for classical angular momenta.
Readings: BFG 9-6
We will apply the recipe for adding angular momentum to more degeneracy-splitting scenarios. We will cover the spin-orbit magnetic coupling associated with the "fine structure" seen in atomic spectra, even in the absence of external magnetic fields, and then the "hyperfine structure" associated with interaction of nuclear and electron spins. Finally I will discuss magnetic resonance imaging (MRI).
This is a currently exciting topic in cosmology research! The lecture will be aimed at undergrads. Please see Dr. Cayon's flyer.
Readings: BFG 10-1 through 10-4
We will discuss how to deal with more than one particle, and how to set up wavefunctions for distinguishable and indistinguishable particles. We'll cover symmetry and antisymmetry of wave functions, bosons and fermions, and the Exchange Symmetry Principle, from which the Pauli Principle follows.
Readings: BFG 10-5, parts of 12-1, 12-2
In the first part of the lecture, we'll explore some consequences of the Exchange Symmetry Principle: we'll look at what happens to particles in a box when the are bosons and fermions, and derive the Fermi energy. In the second part of the lecture, I'll introduce a few terms and concepts needed for discussion of classical (and non-classical) gases.
Readings: BFG 12-3
We will consider the more general case of the Maxwell distribution: the Boltzmann relation. We will look at an example with two discrete states, and I will use a concrete example to motivate how the Boltzmann relation follows from the hypothesis that all microstates accessible to the system have equal probability.
This is a replacement lecture, held during the first 50 minutes of your lab period, in the lab.
This is a replacement lecture, held during the first 50 minutes of your lab period, in the lab (same as Wednesday).
Readings: BFG 12-1, 12-4
We will start to connect this material to an observable: the heat capacity of a gas, which changes according to the number of degrees of freedom for excitation that its molecules have.
Readings: BFG 12-5, 12-6, last part of 12-7
We will discuss the effects of indistinguishability of particles on statistical mechanics. At low temperatures, the energy distribution of fermions is affected by the fact that you can't put more than two particles in the same state: the resulting distribution of energies is the Fermi-Dirac distribution. For bosons, there's no such restriction, and the distribution of energies is called the Bose-Einstein distribution.
Readings: BFG 13-3, 13-4 (lecture treatment will be slightly different)
I will briefly discuss perturbations and cover different kinds of transitions (absorption, spontaneous emission and stimulated emission). We will then cover the basic concepts of a very important application of stimulated emission of radiation: the laser.