QM Lecture 1

LECTURE-1    OVERVIEW: CONTRASTING CLASSICAL AND QUANTUM MECHANICS FORMALISMS 

Objective of this lecture
                                                          Obtaining the equation of motion from general principles 

                                                                            Fermat's Principle of Least Time (Photons)

                                         Hamilton's Principle of least Action (Classical mechanical system of particles)
                                                                                        Lagrangian formulation
                                                                                      Hamiltonian formulation       

                                                                                        Quantum description
                                                        Hamiltonian formalism in the Schrodinger Equation                                        
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1.1      Classical view:  Evolution of the Variational Least Time Principle                                                                                                                            09-26-2022)                                                                              

 
1.2    Contrasting the  (deterministic) classical   and   the  (probabilistic) quantum mechanics   descriptions                                                        (09-26-2022)                                                               
          1.2A   The deterministic character of classical mechanics to predict experimental results
                   Classical description of a state of motion
                   Time evolution of a classical state: the classical action, the principle of least action, Lagrange equations
          1.2B   Absence of trajectories in the quantum behavior of particles.
          1.2C   Probing quantum objects with a classical apparatus
                   Classical mechanics as a requirement and as a limiting case of quantum mechanics
          1.2D   The less detailed quantum mechanics description
          1.2E   The non-relativistic quantum mechanics description

1.3   Probabilistic interpretation of the wavefunction                                                                                                                                                                 (Reading assignment)
          1.3A  Max Born’s probabilistic interpretation of the wavefunction.
          1.3B  The QM wavefunction represents an ensemble of systems
          1.3C  Deterministic evolution of the wave function
          1.3D  Normalization condition for the wave function
                   The Hilbert space
          1.3E  The Philosophy of  Quantum Theory
                   The Niels Bohr and Heisenberg’s school
                   De Broglie and Einstein school
                   Feynman’s alternative formulation of quantum mechanics: Path integrals 

1.4   Amplitude probability:  How does light "really" decides which path to follow? 
          1.4A   Classical view:  Evolution of the Variational Least Time Principle                                                                                             (Reading assignment)
          1.4B   An elementary Quantum Dynamics point of view                                                                                                                              (Reading assignment)

Complements
          C.1  Complex numbers                                                                                                                                                                                                        
          C.2  Representation of travelling harmonic waves in complex variable: PHASORS
                    Addition of waves using complex variables