Thursday 7:00 PM: Urmila / Preeti
Friday 7:00 PM: Saurabh / Dipanjan
Saturday 11:00 AM: Akash / Sarath
Saturday 12:00 PM: Kshitish / Barnali
May 7, 2022 (5:30 PM)
May 21, 2022 (4:00 PM)
Jun 25, 2022 (4:00 PM)
Jul 9, 2022 (4:00 PM)
Complex numbers, probabilistic interpretation of the wave function
Quantum mechanical operators, eigenvalues and eigenfunctions
Orthogonal functions, average values of an observable, time evolution of the wave function, particle in a one-dimensional box
Quantum uncertainty (using the example of the particle in a box)
Lecture 1: Chemistry is governed by electrons. Quantum mechanics is necessary to understand behavior of electrons. Why is there structure when matter is mainly empty space. Planck's constant is obtained by fitting a theory of black body radiation to experiment. The postulational approach to quantum mechanics. Structure of the postulates. Postulate 1 -- the wave function.
Lecture 2: The wave function is a complex valued function. The wave function contains information about the distribution of position of the particle. Probability density. Introduction to complex numbers. Properties of a wave function.
Lecture 3: Postulate 2 -- operators corresponding to observables. All operators can be constructed using the position and momentum operators which are defined. Kinetic energy, potential energy and Hamiltonian (total energy) operator.
Lecture 4: Postulate 3 -- eigenvalues are obtained when a property is measured. Eigenfunctions and eigenvalues. Quntum mechanical operators are linear and Hermitian.
Lecture 5: Hermitian operators have real eigenvalues and orthonormal eigenfunctions. Postulate 4 -- average value of an observable. Postulate 5 -- the wave function evolves according to the Schrodinger equation. The Hamiltonian operator determines the evolution of the wave function.
Lecture 6: Dirac notation. If the Hamiltonian does not depend on time, the solution of the Schrodinger equation reduces to solving the eigenvalue equation of the Hamiltonian. Stationary states.
Lecture 7: The particle in a box / Particle in an infinite square well. Eigenvalues and eigenfunctions of the Hamiltonian.
Lecture 8: Particle in a box: Normalization of the eigenfunctions. Visualizing eigenfunctions. A model for certain chemical systems. Time evolution of wave functions.
Lecture 9: Particle in a box: Wave particle duality. Schrodinger's cat. Quantum uncertainty.
Lecture 10: Quantifying uncertainty. Particle in a 2-D box. Degenerate eigenfunctions.
Lecture 11: Symmetry is the origin of degeneracy. Visualizing eigenfunctions of the 2-D box. Particle on a ring. Connection between particle on a ring and the hydrogen atom. Schrodinger equation for a particle on a ring.
Lecture 12: Particle on a ring: Eigenvalues and eigenfunctions. Visualizing eigenfunctions. Angular momentum uniquely identifies the eigenfunctions. Spherical coordinate system.
Lecture 13: Particle on a sphere: Quantization of speed of rotation (i.e. kinetic energy or magnitude of angular momentum) and plane of rotation (i.e. the Lz component of angular momentum). Eigenvalues and eigenfunctions of the particle on a sphere.
Lecture 14: Hydrogen atom: Hamiltonian, eigenvalues and eigenfunctions. 3 quantum numbers. Radial part of the eigenfunctions. Radial probability density. Radial nodes.
Lecture 15: Hydrogen atom: Angular part of the eigenfunctions. Shape of the orbitals. Visualization of orbitals in 3D and as a function of time. Closing remarks.