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