# Projects: Education

### Exam Study Material:

Here are some things to help you study for physics PhD qualifying exams.

#### Typed-up Exams

We usually just get photo copies of the exams, but they can be kind of ugly and spaced such that you can't write your answer on the question page. Also, there are annoying typos and inconsistencies in format. So Chris Clark, Eric Angle, and I typed up these clean versions of the exams that are ideal (when the quesion isn't too long) for writing answers on. (Some typos are retained because they give you a real flavor of the exam: there are always typos and sometimes mistatements. Minor typos are usually corrected and major ones retained.) In reverse chronological order:

- [pdf] 2007 Spring
- [pdf] 2006 Fall
- [pdf] 2006 Spring
- [pdf] 2005 Fall
- [pdf] 2005 Spring
- [pdf] 2004 Fall
- [pdf] 2004 Spring
- [pdf] 2003 Fall
- [pdf] 2003 Spring
- [pdf] 2002 Fall
- [pdf] 2002 Spring
- [pdf] 2001 Fall
- ...
- [pdf] 1996 Fall
- [pdf] 1996 Spring
- [pdf] 1995 Fall
- [pdf] 1995 Spring

Please let me know if you notice a problem with the exams (a typo originating with us, omissions, etc.) or have any other concerns (an opinion about how the typos of the exam itself should be handled, you think the font should be larger, etc.).

#### Solutions

Here are some solutions that I wrote up. I apologize for writing close to the edge of the paper on some of them; that makes them not completely printable. Please let me know if you find any errors.

##### 2007 Spring

1. | QM: | - (Hydrogen atom in weak magnetic field...) | |

2. | QM: | - ("irrotational" l=0 bound states for a spherical Dirac shell potential...) | |

3. | QM: | [pdf] Hydrogen atom state quantum numbers and operator matrix elements | (Quasi-Repeated) |

4. | QM: | - (Particle scattering, cross section...) | |

5. | QM: | - (1D conical well, variational method using Gaussian) | |

6. | SP: | [pdf] (v1), [pdf] (v2) N noninteracting distinguishable harmonic oscillators, heat capacity at extreme temperatures | |

7. | SP: | - (System with given equation of state, entropy and free energies) | |

8. | EM: | [pdf] Black body spectral energy density, energy density temperature dependence | |

9. | EM: | - (DNA) | |

10. | EM: | - (Scattering) | |

11. | EM: | - (Electron beam) | |

12. | EM: | - (Plane em wave...) | |

13. | SP: | - (Potential for cylinder-halves with potential difference) | |

14. | SP: | - (Current-carrying wire in different frames, forces on charges, etc..) |

##### 2006 Fall

1. | QM: | [pdf] Wavefunction in a spherically symmetric potential | |

2. | QM: | [pdf] Identical spin-1/2 particles in a potential well, perturbative interaction | |

3. | QM: | [pdf] Solar neutrino oscillation | (Quasi-Repeated) |

4. | QM: | [pdf] - Anticommuting creation and annihilation operators | |

5. | QM: | [pdf] Neutron scattering off of Yukawa potential, Born approximation, low energy | (Repeated) |

6. | SP: | - (Spin magnetization and magnetic Gibbs potential...) | |

7. | SP: | - (Heat capacity of a relativistic gas...) | |

8. | SP: | [pdf] Fluctuations and compressibility of a grand canonical ensemble of particles | (Questions) |

9. | SP: | - (Chandrasekhar limit of a white dwarf) | |

10. | EM: | [pdf] (v1), [pdf] (v2) Charge distribution of a spherically symmetric potential | |

11. | EM: | - Reflection and transmission coefficients, normal incidence and s-polarization | (Repeated) |

12. | EM: | - (An electron in fields; constants of motion) | |

13. | EM: | - (Multipole radiation...) | |

14. | EM: | [pdf] Vector potential and magnetic field of a rotating charged spherical shell |

##### 2006 Spring

1. | QM: | [pdf] Stationary electron spin precession | (Repeated) |

2. | QM: | [pdf] 1D QSHO state investigation | |

3. | QM: | [pdf] - (Linear Stark effect?, degenerate perturbation theory) | |

6. | SP: | -(Bose-Einstein condensation for relativistic, conserved bosons (spinless, d-D)) | (Repeated) |

10. | EM: | - (Electrically induced E-forces between hemispheres) | |

11. | EM: | Induction in a cylindrical conductor | |

12. | EM: | - (Charged, oscillating balloon radiation) |

##### 2005 Fall

1. | QM: | [pdf] Hydrogen atom state quantum numbers and operator matrix elements | (Quasi-Repeated) |

2. | QM: | [pdf] -(1D QSHO unitary transformation and perturbation) | |

3. | QM: | - (Hydrogen atom decays, selection rules, rates) | |

4. | QM: | [pdf] Energies of 3 distinguishable spin-1/2 particles | (Question) |

5. | QM: | - (Scattering, Born approximation) | |

6. | SP: | - (Star degeneracy pressure, non- and ultra-relativistic) | |

7. | SP: | - (Stretched plastic rod, entropy, temperature, heat capacity) | |

8. | EM: | - (Dispersion, damping in, and power to an anisotropic medium with tensor conductivity) | |

9. | EM: | [pdf] Energy of two localized induced polarizations | |

10. | EM: | [pdf] Plasma frequency, permittivity, measuring distance to pulsar using dispersion | |

11. | EM: | [pdf] Rotating copper ring, damped in magnetic field by Joule heating | (Repeated) |

12. | EM: | - (Magnetized infinite cylinder...) | |

13. | SP: | - (Hydrogen molecule, "ortho" and "para"...) | |

14. | SP: | [pdf] (v1), [pdf] (v2) - (N classical nonrelativistic charged particles in a magnetic field) |

##### 2004 Fall

1. | QM: | [pdf] Singlet, two spin-1/2 particles, spin projection product expectation | |

2. | QM: | [pdf] Perturbative van der Waals dipole interaction in 1D | |

3. | QM: | [pdf] Positronium probability, energies, charge conjugation | |

4. | QM: | - (Hydrogen atom state quantum numbers and operator matrix elements) | (Quasi-Repeated) |

5. | QM: | [pdf] Investigation of a hydrogen atom ("mixed"?) state | |

6. | SP: | - (Specific heats of ideal quantum gases in d-dimensions) | |

7. | SP: | - (Susceptibility of singlet/triplet-state molecules, cooling by adiabatic magnetization) | |

8. | EM: | [pdf] Ferromagnetic fields without free current | |

9. | EM: | [pdf] Fields of a current-carrying wire with capacitor | |

10. | EM: | [pdf] Electric potential of a charge in two media with different permittivities | |

11. | EM: | [pdf] Radiation power dependence (dimensional analysis and general principles) | |

12. | EM: | [pdf] Energies for fixed-target and collider beam experiments | |

13. | SP: | [pdf] Landau-Ginzburg free energy for magnets, heat capacity and critical temperature | (Questions) |

14. | SP: | Average energy per photon in black-body radiation |

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