“Not only is the
― Werner HeisenbergUniverse stranger than we think,it is stranger than we can think.”
About this course:
- Lecturer: Prof. Dr. C. Hanhart, PD Dr. B. Kubis
- Year: 2016/2017
- Difficulty:
- Course page: eCampus
- Tutor: F. Meirinhos
- Literature:
Once more a well-structured course, going into more detail on quantum mechanics, scattering, and many-body theory.
Exercise 1:
Keywords: Lippmann-Schwinger Equation, Hamilton Operator, Potential Operator, T-Matrix, Separable Operator, Residue Theorem, Complex Plane
- Solution of the Lippmann-Schwinger Equation for Separable Potentials
- Integration in the Complex Plane
Exercise 2:
Keywords: First-order Born Approximation, Scattering Amplitude, Yukawa Potential, Born Series, Second-order Born Approximation, Second-order Born Term, Residue Theorem, Optical Theorem, Forward Scattering Amplitude
- The Second-order Born Approximation
Exercise 3:
Keywords: Elastic Scattering, Hard Sphere, Central Potential, Scattering Phase, Spherical Bessel Functions, Spherical Neumann Functions, Partial Wave Scattering Amplitude, Partial Waves, Effective Range Expansion, Scattering Length, Effective Range, Cross Section, Total Elastic Cross Section, Bernoulli Numbers
- Hard Sphere Scattering
Exercise 4:
Keywords: Unitarity, Scattering Matrix, S-Matrix, Forward Scattering Amplitude,
- Unitarity and the Optical Theorem
Exercise 5:
Keywords: Functionals, Functional Derivative, Classical Action Functional, Extremum of the Action, Hamilton’s Principle, Euler-Lagrange Equation
- Derivatives of Functionals
- Euler-Lagrange Equations
Exercise 6:
Keywords: One-dimensional Harmonic Oscillator, Action Functional, Functional Derivative, Physical Path, Delta Functional, Functional Taylor Expansion
- Harmonic Oscillator
Exercise 7:
Keywords: Klein-Gordon Equation, Complex Conjugated Wave Function, Klein-Gordon Four-Current, Continuity Equation, Current Norm, Unphysical Negative-energy Solutions
- Klein-Gordon Equation
Exercise 8:
Keywords: Gamma Matrices, Properties, Anti-commutation Relation, Fifth Gamma Matrix, Trace Identities, Representation Independent, Standard Representation
- Properties of the Gamma Matrices
Exercise 9:
Keywords: Gamma Matrices, Anti-commutation Relation, Standard Representation, Weyl Representation, Dirac Spinors, Charge Conjugation, Stationary States
- Weyl Representation of the Gamma Matrices
- Charge Conjugation
Exercise 10:
Keywords: Dirac Equation, Positive Energy Solution, Gordon Identity, Projection Operators, Spin Sums, Lorentz Transformation, Dirac Spinors, Proper Orthochronous Transformations, Parity Transformation, Transformation Properties, Scalar, Pseudoscalar, Vector, Pseudovector, Axial-Vector, Tensor
- Gordon Identity
- Projection Operators for Positive/Negative Energy States
- Lorentz Transformation of Bilinear Forms
Exercise 11:
Keywords: Proper Unitary Transformation, Effective Hamiltonian, Fine Structure of the Hydrogen Atom, Wave Function at the Origin
- Foldy-Wouthuysen Transformations
Exercise 12:
Keywords: Single-particle Operators, Bosons, Creation Operator, Annihilation Operator, Two-particle Operators, Commutation Relations, Particle Number Operator
- Single/Two-particle Operators for Bosons
- Particle Number Operator
Exercise 13:
Keywords: Creation Operator, Annihilation Operator, Two-particle Operator, Single-particle Wave Function, Field Operators, Bosons and Fermions, Commutation Relations, Anti-commutation Relations
- Momentum Representation
Exercise 14:
Keywords: Non-interacting Fermion Gas, Identical Fermions, Particle Number Density, Field Operators, Annihilation Operator, Creation Operator, Single-particle Wave Function, Static Structure Function, Infinite Volume Limit
- Static Structure Function
Lifesaver!