TABLE OF CONTENTS
COURSE QUANTUM THEORY 1
Course: P. J. H. Denteneer, Fall 2001
Lecture notes (Chapter I to V in Dutch!): R. H. Terwiel, Leiden 1990/2000

  
  

	I.  REPRESENTATIONS
§1.	The essence of the theory of representations	8
§2.	Different representations of Pauli theory	10
§3.	The momentum-representation formulation of Schrödinger theory
	for a particle without spin	15
§4.	The $n$-representation for the harmonic oscillator	18
	II.  ABSTRACT FORMULATION
§1.	State vectors and Dirac notation	22
§2.	Projection operators and completeness relations;
	density operators en density matrices	28
§3.	Abstract formulation of quantum mechanics	34
	III.  SCHRÖDINGER-, HEISENBERG- EN INTERACTION PICTURES
§1.	Differential and integral equations for operators	43
§2.	The Schrödinger picture	48
§3.	The Heisenberg picture	51
§4.	The interaction picture	53
	IV.  QUANTUM THEORY OF RADIATION
§1.	Hamilton description of a classical radiation field	60
§2.	Quantisation of the radiation field	64
§3.	Planck's radiation law (1)	69
§4.	Radiation transitions in (quasi-) one-electron atoms	70
§5.	Planck's radiation law (2)	79
§6.	Scattering of radiation by free electrons	81
	V.  SECOND QUANTISATION
§1.	Introduction	87
§2.	The $N$-boson system	88
§3.	The many boson system	96
§4.	Identical spin 0 particles	103
§5.	The $N$-fermion system	116
§6.	The many fermion system	120
§7.	Identical spin ${\textstyle \frac{1}{2}}$ particles	123
§8.	Bose-Einstein and Fermi-Dirac distributions	127
	Exercises with Chapter I to V	133
	Solutions to exercises Chapter I to V	148

	VI.  PATH INTEGRALS
§1.	The multislit, multiscreen experiment	162
§2.	The transition amplitude	163
§3.	Evaluation of the transition amplitude for short time intervals	163
§4.	The path integral	164
§5.	Evaluation of the path integral for a free particle	166
§6.	Why some particles follow the path of least action	167
§7.	Quantum interference due to gravity	169
§8.	Summary	170
	Exercises with Chapter VI	172