# Physics 143 Fall 2007Syllabus and Schedule

I will include here readings for each lecture, as well as any relevant documents or links. Always under construction! This page is subject to modification as the semester progresses-- often topics can take longer than initially planned, and we may make interesting diversions if opportunities arise. The likely material to be covered can be found here. Readings and more details for a given lecture will appear at a day or two before the lecture, and I may also add notes and links after a given lecture has taken place.

## Monday, August 27: Lecture 1   Introduction and Review

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.

• Traveling and standing wave animations shown in class. (This site shows how you can create them yourself with Maple if you are so inclined!)
• A derivation of the wave equation for the vibrating string, for those interested.
• d'Alembert's general solution to the wave equation, for those interested.
• Note on BFG, p. 10: the statement "The frequency f=w/2pi is determined by the wave equation" is not really correct (or at least misleading.) It's really v that's given by the wave equation; w is given by kv. The subsequent statement that lambda is determined by the boundary conditions is correct. But as lambda varies, so does w according to kv= 2pi v/lambda.
• FAQ 1

## Wednesday, August 29: Lecture 2   Interference

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.

## Friday, August 31: Lecture 3   More on Interference and Diffraction

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.

## Monday, September 3: Lecture 4   Single Slit Diffraction, Thin Film Interference

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.

## Wednesday, September 5: Lecture 5   Introduction to Relativity

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!)

## Friday, September 7: Lecture 6   Consequences of Special Relativity

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.

## Monday, September 10: Lecture 7   More Consequences of Special Relativity

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.

## Wednesday, September 12: Lecture 8   Relativistic Energy and Momentum

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.

## Friday, September 14: Lecture 9  Relativity Examples: Binding Energy and Mass

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.

## Monday, September 17: Lecture 10   Introduction to Quantum Physics

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.

## Wednesday, September 19: Lecture 11   The Quantum Nature of Light

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.

## Friday, September 21: Lecture 12   Particles as Waves and Waves as Particles

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.

## Friday, September 28: Guest Speaker   Prof. Oh

Professor Oh, Physics Department Director of Undergraduate Studies, will be guest lecturer.

## Monday, October 1: Lecture 14   The Bohr Atom

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.

## Wednesday, October 3: Lecture 15   The Schrödinger Equation

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.

## Friday, October 5: Lecture 16   More on the Schrödinger Equation

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".

## Wednesday, October 10: Lecture 17   More Schrödinger Examples

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.

## Friday, October 12: Lecture 18   Wave Packets

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.

• Some links for those interested in Fourier analysis:
• FAQ 18

## Monday, October 15: Lecture 19   The Uncertainty Principle

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.

## Wednesday, October 17: Lecture 20   The Energy-Time Uncertainty Principle, and Potential Barriers

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.

## Friday, October 19: Lecture 21   More on Scattering from a Barrier: Quantum Tunneling

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.

• There is a typo in BFG, first equation on p. 211: it should read P_i = F_i exp(-2 kappa_i Delta x_i). The other equations are correct. (Note that the width of the barrier is Delta x=2a, which is why there's a factor of 4 in the equations which have a.)
• FAQ 21

## Monday, October 22:   TUNL Tour

Prof. Calvin Howell will give a tour of the Tri Universities Nuclear Lab on campus. Please meet him in your regular classroom.

## Wednesday, October 24:   Visit to JET Lab

Prof. John Thomas will give a presentation about his research in quantum optics and a tour of his lab. Please meet him in your regular classroom.

## Friday, October 26:  Tour of the Duke Free Electron Laser Lab

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).

## Monday, October 29: Lecture 22  Bound States

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.

## Wednesday, October 31: Lecture 23   The Scanning Tunneling Microscope, and the Schrödinger Equation for a Central Potential

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.

## Friday, November 2: Lecture 24   Angular Momentum

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.

• There is a mistake in BFG, equation 9-10: in the third term on the left hand side, the coefficient of F(theta) should be -m^2 csc^2(theta).
• Some reference info on spherical harmonics.
• If you want to see the details of where the Legendre polynomials, and the corresponding conditions on m and l, come from, check out Pauling and Wilson, Introduction to Quantum Mechanics, Dover, 1935, Chapter V.
• FAQ 24

## Friday, November 9: Lecture 26  More on Angular Momentum, and the Hydrogen Atom

Substitute lecturer: Prof. Chandrasekharan

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.

• If you want to see the details of where the Laguerre functions come from, you can find that too in Pauling and Wilson, Introduction to Quantum Mechanics, Dover, 1935, Chapter V.

## Monday, November 12: Lecture 27   The Zeeman Effect

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.

## Wednesday, November 14: Lecture 28   Spin

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.

• Mistake in BFG: in Figure 9-15, the positive m and m_s values should have higher energy.
• FAQ 28

## Friday, November 16: Lecture 29   More Degeneracy Splittings: Spin-Orbit Coupling, Hyperfine Structure, and Magnetic Resonance Imaging

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).

## Monday, November 26: Lecture 30   Many Particles and Exchange Symmetries

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.

## Wednesday, November 28: Lecture 31   Fermi Energy, Classical Gases

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.

## Replacement Lecture 32   Boltzmann Statistics

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.

## Thursday, November 29: Replacement Lecture 32   Boltzmann Statistics

This is a replacement lecture, held during the first 50 minutes of your lab period, in the lab (same as Wednesday).

## Friday, November 30: Lecture 33   Heat Capacities, Equipartition

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.

## Monday, December 3: Lecture 34   Fermi-Dirac and Bose-Einstein Distributions

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.

## Wednesday, December 5: Lecture 35   Transitions and Lasers

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.