Students are welcome to suggest topics of their own. You should do this by sending Prof. Zwiebach a brief paragraph by email, summarizing the topic. There is no separate deadline by which you must do this, but note that your complete proposal is due on Wednesday during week 8. At the time you submit your proposal, you should already know that your choice of topich has been approved. (Note that your writing assistant may nevertheless require you to revise your proposal.)

Below is a list of possible topics:

- The allotropic forms (ortho/para) of hydrogen.
- Nuclear Magnetic Resonance. Since we have spent some time on this in class, you should go beyond it. Some possibilities are dynamic nuclear polarization, nuclear quadrupole resonance, composite pulses, spin-echo, liquid vs solid-state NMR, relaxation mechanisms, or its application in particular experimental/medical contexts.
- Magnetic monopoles, gauge invariance, and the Dirac quantization condition for the magnetic charge of a magnetic monopole.
- Scattering off a magnetic flux tube.
- Bell’s theorem and its variants. Again since we have seen this in
*8.05 Quantum Physics II*, you will need to go beyond it. Some possibilites are the Tsirelson bound, the question of loopholes and/or various experimental tests or a discussion of other nonlocal games. - Neutrino oscillations in vacuum.
- Oscillation phenomena involving kaons and/or B mesons.
- The solar neutrino problem.
- The shell model of nuclear structure.
- Application of random matrix theory to nuclear physics.
- The properties of the deuteron.
- The α-decay of
^{238}U. - The rotational and vibrational spectrum of diatomic molecules.
- Dynamical
*SU*(*n*) symmetry of the harmonic oscillator in*n*dimensions. - Supersymmetric quantum mechanics, beyond what we did in 8.05.
- The Lamb shift in hydrogen —evidence that relativistic quantum mechanics must be replaced by quantum field theory. (This is an example of a topic where you will not be able to give a complete derivation of the effect, but where those of you interested in the history of physics could write a paper which explains the quantum physics more qualitatively while at the same time describing the experiments and the history in full.)
- The non-relativistic quark model of the proton, neutron and related particles.
- Isospin—a quantum symmetry of elementary particles.
- The 21 cm line of hydrogen and its role in astrophysics.
- The Casimir effect.
- Feynman’s path integral approach to quantum mechanics, and its application to several problems of your choice which we have previously analyzed using other methods. (If you choose a formal topic like this, about a method rather than a phenomenon or problem, you must take it far enough to show how the method is applied to a phenomenon or problem.)
- The van der Waals force between hydrogen atoms in excited states.
- Quantum computing. This is too broad a topic for a paper, but you might discuss a proposal for building quantum computers, some particular algorithm (not Grover, Simon or Shor, since those may appear in lecture), or some other topic such as quantum error correction.
- Quantum cryptography.
- Bose-Einstein condensation.
- Integer and/or Fractional Quantum Hall Effect.
- Photonic Crystals.
- Quantum Dots.
- Crystallographic defects, e.g. NV centers in diamond.
- The deHaas van Alphen effect as a tool for measuring the shapes of Fermi surfaces in metals.
- Periodic potentials and band structure in 3D.
- Graphene and pseudo-spin.
- Some topic within quantum statistical mechanics. Possibilities include the quantum Ising model, quantum Monte Carlo, quantum phase transitions, von Neumann entropy or the spectrum of black body radiation. (You could also include an account of how Planck was led to discover quantum mechanics in the first place, or of how the spectrum of black body radiation appears in the cosmic three-degree background radiation.)
- Decoherence in some physical system.
- Optical pumping, masers, lasers.
- Masers in astrophysics.
- Applications of the semiclassical approximation.
- The Josephson effect.
- The Wigner-Eckart theorem.
- Fractional statistics in two dimensions.
- Wigner functions and applications.
- Tunneling, beyond the discussion in class. The Euclidean approach; effects of nonzero temperature.
- The microscopic origin and effects of quantum dissipation, for example on tunneling.
- Inverse scattering method and its application to solitons.
- The Dirac equation and its application to hydrogen.
- … and so on.