Physics PhD Qualifiers

External Resources

• Bertrand's UCLA Solutions Site
• UCSD Solutions Site
• Lim Yung-Kuo's Solutions Books

Typed-up Exams

• Spring 2002
• Fall 2002
• Spring 2003
• Fall 2003
• Spring 2004
• Fall 2004
• Spring 2005
• Fall 2005
• Spring 2006

Fall 2002 Solutions

• 1. Stern-Gerlach (spin precession)
• 2. Landau levels
• 3. Quadratic stark effect (perturbation theory)
• 4. Hydrogen-like atom (virial theorem)
• 5. Hydrogen molecular ion
• 6. Fermion gas
• 7. 2D molecular chain
• 8. Radiating charges (larmor formula)
• 9. Electromagnet (inductance)
• 10. Charge in sphere (spherical method of images)
• 11. Measurement techniques
• 12. Resistor network
• 13. Ideal gas with internal energy states
• 14. Potts model and mean-field theory

Spring 2003 Solutions

• 1. Simple harmonic oscillator transitions
• 2. Ground state energy of two interacting spins
• 3. Coherent state of simple harmonic oscillator
• 4. Two electrons on two sites
• 5. Half-linear well (WKB Approximation)
• 6. N lattice sites and N atoms
• 7. Gas of atoms and molecules
• 8. Variable Capacitor
• 9. Conducting plane with split potential
• 10. X-Ray mirror critical angle
• 11. Secret LC circuit
• 12. Field of a uniformly magnetized sphere
• 13. Specific heat of non-conserved bosons
• 14. Equilibrium with a reservoir

Fall 2003 Solutions

• 1. Two spin half particles
• 2. Scattering off double delta potential
• 3. Half harmonic oscillator
• 4. Repeated measurements
• 5. Hydrogen transitions (time-dependent perturbation theory)
• 6. Gas of non-conserved bosons (grand canonical partition function)
• 7. Ideal gas in a gravitational field
• 8. Vacuum Diode
• 9. Impedance of transmission lines
• 10. Potential in a wedge
• 11. Plasma dispersion relation
• 12. Electron beams
• 13. Cells and partitions
• 14. Ising model with three spin states

Spring 2004 Solutions

• 1. Clebsch-Gordan table
• 2. Hydrogen transitions (time-dependent perturbation theory)
• 3. Gaussian wave function
• 4. Neutrino oscillation
• 5. Finite square well transmission coefficient
• 6. Bose-Einstein Condensation
• 7. Impurity trap
• 8. Point charge and conducting sphere
• 9. Conducting plane with split potential
• 10. Cylindrical capacitor in a magnetic field
• 11. Plasma index of refraction
• 12. Fields of a charge in motion
• 13. Free expansion of a van der Waals gas
• 14. Clusters in a lattice

Fall 2004 Solutions

• 1. Product of spin in different directions
• 2. 1D van der Waals force (perturbation theory)
• 3. Positronium ground state (canonical coordinates)
• 4. Hydrogen atom matrix elements
• 5. Simple harmonic oscillator
• 6. Heat capacity of quantum gases
• 7. Magnetic susceptibility in singlet-triplet molecules
• 8. Fields of a uniformly magnetized sphere (magnetic scalar potential)
• 9. Displacement current
• 10. Point charge and two half-spaces of different permittivity
• 11. Larmor formula derivation
• 12. Electron positron annihilation (velocity addition formula)
• 13. Landau-Ginzburg free energy of a magnet
• 14. Average energy per photon in blackbody radiation

Spring 2005 Solutions

• 1. Quadratic stark effect (perturbation theory)
• 2. 1D attractive potentials have bound states (virial theorem)
• 3. Hard sphere scattering cross section (partial wave analysis)
• 4. Spin precession
• 5. Hydrogen atom wave function (spherical harmonics)
• 6. Free expansion of ideal gas
• 7. Doppler effect (maxwell-boltzmann distribution)
• 8. Potential in a wedge with dielectric
• 9. Magnetic field of infinite current sheet
• 10. Relativistic gyrofrequency
• 11. Plane wave reflection
• 12. Ring spinning in magnetic field
• 13. 1D Ising model
• 14. Photon gas

Spring 2006 Solutions

• 1. Spin precession
• 2. Simple Harmonic Oscillator
• 3. Linear Stark Effect (Degenerate Perturbation Theory)
• 4. Spherical Potential Scattering (Born-Oppenheimer Approximation)
• 5. Energy levels of mass on a ring
• 6. Bose-Einstein Condensation
• 7. Magnetic Susceptibility
• 8. System of particles with two internal energy states
• 9. Statistical Weight
• 10. Force between hemispheres (Spherical Method of Images)
• 11. Inductance in a cylinder
• 12. Radiation of oscillating balloon
• 13. Orbit of relativistic particle in a magnetic field
• 14. Plane wave damping