Quantum Mechanics

1. Fundamental Concepts - Mathematics, Matrix Mechanics, Bra-ket notation

2. Quantum Dynamics

   1. Time Evolution & Schrodinger Equation

   2. Schrodinger & Heisenberg Picture

   3. Simple Harmonic Oscillator

   4. Scrodingers Wave Equation

   5. Elementary Solutions to Scrodingers Wave Equation

   6. Propagators & Feynmann Path Integrals

   7. Potentials & Gauge Transformations

3. Theory of Angular Momenta

   1. Rotations and Angular Momentum Commutation Relations

   2. Spin 1/2 systems an d Finite Rotations

   3. SO(2), SU(2), and Euler Rotations

   4. Density Operators and Pure versus Mixed Ensembles

   5. Eigenvalues and Eigenstates of Angular Momentum

   6. Orbital Angular Momentum

   7. Scrodingers Equation for Central Potentials

   8. Addition of Angular Momenta

   9. Schwingers Oscillator Model of Angular Momentum

   10. Spin Correlation Measurements and Bell's Inequality

   11. Tensor Operators

4. Symmetry in Quantum Mechanics

1. Approximation methods

   1. Time-Independent Perturbation Theory: Nondegenerate Case

   2. Time-Independent Perturbation Theory: The Degenerate Case

   3. Hydrogen-like Atoms: Fine structure and the Zeeman Effect

   4. Variational Methods

   5. Time-Dependent Potentials: The Interaction Picture

   6. Hamilitonians with Extreme Time Dependence

   7. Time-Dependent Perturbation Theory

   8. Applications to Interactions with the Classical Radiation Field

   9. Energy Shift and Decay Width

2. Scattering Theory

   1. Scattering as a Time-Dependent Perturbation

   2. The Scattering Amplitude

   3. The Born Approximation

   4. Phase Shifts and Partial Waves

   5. Eikonal Approximation

   6. Low-Energy Scattering and Bound States

   7. Resonance Scattering

   8. Symmetry Considerations in Scattering

   9. Inelastic Electron-Atom Scattering

3. Identical Particles

   1. Permutation Symmetry

   2. Symmetrization Postulate

   3. Two-Electron System 

   4. The Helium Atom

   5. Multiparticle States

   6. Density Functional Theory

   7. Quantum Fields

      1. Second Quantization

      2. Dynamical Variables in Second Quantization

      3. Example: The Degenerate Electron Gas

   8. Quantization of the Electromagnetic Field

4. Relativistic Quantum Mechanics

Quantum Mechanics Notes

• Quantum Formula Sheet - Kayla

• Why is the Yukawa Potential Important? - Kayla

• Deriving Derivative Condition with Delta Potential - Kayla 

• Scattering - Resonances (Shankar Notes) - Kayla

• Example problem (3.2 Zettili) which illustrates how to calculate probabilities of being in a final state given an initial state - Kayla

• The Time Evolution of Stationary States - Zettli Chapter 3 Notes - Kayla

• Example 9.1: Charged Oscillator in an External Electric Field (Perturbation Theory) - Kayla 

• Dirac Equation Notes - Kayla

• Scattering Notes

  • Introduction to Scattering Theory (Classical)/ Going from the CM frame to the Lab frame - Kayla

  • Introduction to Quantum Mechanical Scattering in the Center of Mass Reference Frame - Kayla

  • Introduction to the Scattering Amplitude and reason for its importance - Kayla

  • Finding the Green's Function to Obtain a General Solution for the wavefunction to include incident wave and scattered wave - Kayla 

  • Iteratively Approximating Scatter Wavefunction Solution - Kayla

  • Using the Born Approximation to Calculate the Scattering Amplitude and Differential Cross Section - Kayla 

  • When is the Born Approximation Valid? - Kayla

  • Partial Wave Analysis to Solve Quantum Mechanical Scattering Problems - Kayla

  • QM Inelastic Scattering - loss of flux through cross section - Kayla

Quantum Mechanics Problems

• Quantum Past Problems Review Sheet - Kayla

• Chapter 1 Sakurai Problems - Kayla

• Sakurai Solution Manual