Quantum Mechanics: Fundamental Principles and Applications

Linear algebra                            
 Linear vector spaces                                          
 Linear independence                                          
 Inner product                                              
 The dual space                                         
 Non-orthogonal basis sets                                   
 Operators                                                
 Eigenvalues and eigenvectors:                                 
 Non-orthogonal basis vectors                                 
 Projection operators:                                      
 Spectral representations:                                    
 Basis transformations                                     
 Commuting operators                                     
 Maximal sets of commuting operators                            
 Infinite dimensional spaces                                       
   Translation of the coordinate system                             
   Measurement                                              
   The uncertainty relation                                    
   Time in non-relativistic quantum mechanics  
 Canonical quantization 
 Classical mechanics review      
 Symmetries of the action  
 Galilean transformations   
 Canonical quantization postulates 
 The Heisenberg picture   
 The Schrodinger picture  
  Canonical transformations      
  Schwinger’s transformation theory 
 Path integrals
 Space-time paths       
 Some path integrals     
 Matrix elements of coordinate
 Generating functionals    

Closed time path integrals 
Initial value conditions   
Connected Green functions
Classical expansion     
Some useful integrals    
 In and Out states
 The interaction representation                                     
 The time development operator                                    
 Forced oscillator                                            
 Density matrix formalism                          
 Classical theory                                             
 Classical time development operator                             
 Classical averages                                        
 Classical correlation and Green functions                          
 Classical generating functional                                
 Quantum theory                   
 Thermal densities                          
 The canonical ensemble                            
 Ensemble averages                               
 Imaginary time formalism                           
 Thermal Green functions                           
 Path integral representation                          
 Thermovariable methods   
 Green functions
 Identical particles
 Coordinate representation     
 Occupation number representation
 Particle fields            
 Hamiltonian                                        
 Symmetries                          
 Galilean transformations                                        
 The Galilean group                                       
 Group structure                                        
 Galilean transformations                                        
 Phase factors for the Galilean group                             
 Unitary transformations of the generators                          
 Commutation relations of the generators                           
 Center of mass operator                                    
 Casimir invariants                                       
 Extension of the Galilean group                                
 Finite dimensional representations                              
 The massless case                                       
 Time translations                                            
 Space translations and boosts                                     
 Rotations                                                
 The rotation operator                                       
 Supersymmetry                   
 Grassmann variables                                          
 Superspace and the D-N supersymmetry group                          
 D-N supersymmetry transformations in quantum mechanics                   
 Supersymmetric generators                                      
 R-symmetry                                               
 Extension of the supersymmetry group                                
 Differential forms     
 Rotations of the basis sets  
General Galilean transformations  
Improper transformations      
 Parity             
 Time reversal         
 Charge conjugation      
Scale and conformal transformations
 Scale transformations    
 Conformal transformations 
 Wave equations
 Scalars            
 Spinors           
 Spinor particles   
 Spinor antiparticles 
 Vectors           
 Massless wave equations  
 Massless scalers   
 Massless vectors  
 Finite quantum systems
 Diatomic molecules  
 Periodic chains    
 Linear chains     
 Impurities       
 Bound state  
 Scattering    One and two dimensional wave mechanics
 Introduction        
 Transmission of a barrier           
 Wave packet propagation           
 Time delays for reflection by a potential step