In this page you will find:

• List of topics of QM-II, QM-III and QM-Advanced courses.
• General checklist of topics in Quantum Mechanics. 

It is assumed that the student has taken the introductory course QM-I. Hence the student should be familiar with Dirac notations and with the elementary solutions of the Schrodinger equation: Simple potenials in one dimension; Harmonic oscillator; Hydrogen atom.

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QM-II topics  / first part

• Dirac notations, the continuum limit.
  
• The fundemental postulates of Quantum mechanics
  
• Magentic field  (gauge, AB, Landau, Hall)
  
• Group theory, Representations, Rotations, Spin
• Addition of angular momentum (elementary level)
  

QM-II topics /  second part

• Perturbation theory for eigenstates (up to 2nd order)
• Perturbation theory for time evolution (first order)
  
• Wigner decay, FGR transtions, scattering by Born formula
  
• The adiabatic picture (elementary level)
  

QM-III topics / first part  (For more details see below)

• Path integrals
  
• The resolvent and Green functions
  
• Perturbation theory to infinite order
  
• Semiclassical approximations (brief).
• Scattering theory (S matrix, partial waves).

QM-III topics / second part

• Transformations of H and invariance
• Addition of angular momentum etc.
• Identical particles (elementary level + Fock space)
• Quantization of the EM field
  

 
QM - advanced topics (For optional topics see below)

• The probability matrix
  
• Theory of quantum measurements
• Wigner function and Wigner-Weyl formalism
  
• Schrodinger cat, EPR, Bell...
  
• Quantum Computation.
• Adiabatic processes. Berry phase.
• Linear response  theory (Kubo formula).
• Born-Oppenheimer picture.

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Elaborated list of topic for the first part of the QM-III course:

• The evolution operator for constant H
• diagonalization
• space representation U(x|x0)
• for free particle
• for bounded particle (oscillator)
• for short times
• Feynman path integral
• Semiclassical evaluation

• The resolvent G(z)
• for closed systems
• for open system (analytical continuation)
• Green functions
• for free particle in 1D/2D/3D
• Green theorem
  

• perturbation theory for G(z)
• perturbation theory for U

• perturbation theory for scattering states
• the asymptotic wave function
• cross section
• S matrix via the T expansion

• the S-matrix formalism
• S matrix for a wire with delta function
• S matrix for several connected wires / leads
  
• S matrix for spherical geometry
• unitarity and optical theorem

• phase shifts
• scattering from a sphere / well
  
• resonances
  
• Born approximation for the phase shifts

• Fisher Lee relation
• the R matrix approach

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Elaborated list of optional topic for the QM-advanced course:

• Banded matrices (Wigner/Anderson models)
• Random matrix theory and Quantum Chaos

• Theory of conductance and quantum pumping
  

• Born-Oppenheimer approximation
• Feynman-Vernon Formalism
• Master equations
• Dissipation and Decoherence

• Two level system -  The spin boson model
• Multi level system -  Pauli Eq.
• Damped particle -  Fokker-Plank Eq.
• Reaction rate theory, Kramer