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## Tuesday, March 31, 2009

### Free Physics Video Lectures

Hi everyone! This month I have another nice list of physics video lectures. This is the 8th post about physics videos. See the first seven here: 1, 2, 3, 4, 5, 6, 7.

This post will cover quantum mechanics, quantum physics, classical physics, classical mechanics, chaos, fractals and dynamical systems, linear dynamical systems, heat and mass transfer and general relativity.

Quantum Physics

31 lectures, Prof.V.Balakrishnan, Department of Physics, IIT Madras

Course topics:
Introduction to Quantum Physics. Heisenberg's uncertainty principle. Introduction to linear vector spaces. Characteristics of linear vector spaces. Functions in a linear vector space. Linear operations in a linear vector space and their matrices. Classical vs Quantum Mechanics. Schrodinger equation. Schroedinger equation in time-independent vector potential. Path Integral Approach to Quantum Mechanics. Probability density and probability current. Potential wells, bound states, delta-function potentials. Bloch theorem. Angular momentum: Symmetry and invariance, group theory and rotations. Addition of Angular Momentum. Groups SO3, SU2. Schrodinger Equation in 3 dimensions. Hydrogen atom. Introduction to Scattering Theory: Partial wave expansion, Born Approximation, effective range approximation. The WKB approximation. WKB method. Bohr-Sommerfeld quantization. Quantum dynamics. Exchange operator, symmetrization and antisymmetrization. Fermions in a box at zero temperature. The Adiabatic and Born-Oppenheimer Approximations. Time-independent Perturbation Theory. Time-dependent Perturbation Theory. Symmetries in Quantum Mechanics.

Quantum Mechanics

10 videos, taught by Leonard Susskind, the Felix Bloch Professor of Physics at Stanford University.

Course topics (approximate):
Dilemmas of classical physics. Energy quantization. Boltzmann distribution. Energy of harmonic oscillator. Equipartition. Specific heat of solids. Blackbody radiation. Quantization of normal modes. Wave equation. Normal modes of cavity. Periodic boundary conditions. Counting modes. Planck law. Other early evidence for quantum behavior. Photoelectric effect. Ritz principle. Bohr model. Motion of wave packet. Electrons as waves. Schrödinger equation. Dynamics of Schrödinger's ψ-function. Spherically symmetric potential (H-atom). 1D simple harmonic oscillator. Particle in electromagnetic field. Schroedinger equation II. Probabilistic interpretation of ψ-function. Fourier transform. Measuring a particle's momentum. Uncertainty principle. Operator formalism I. Momentum operator. Expectation values. Inner products. Hermitian adjoint. Eigenstates and eigenvalues. Operator Formalism II. Completeness. Measurement. Parity. Hilbert space and matrix mechanics. Dirac's bra and ket notation. Postulates and probability. Position representation. Angular Momentum I. Orbital angular momentum operators L-eigenvalues from ladder operators. Eigenvalues from Shrodinger equation. Commutation relations. Spherical potential. L-generates rotations. Angular momentum II. Central forces & pseudopotential. H-atom bound states. QM 2-body problem. Reduction to 1-body problem. Spin I. Electron spin. Pauli spin matrices. 2 spin-1/2 particles. Many particles. Electron magnetic moment, precession. Spin II. Absprption. Resonant scattering. T-matrix. Measurements. Superposition. Collapse of wave function. Role of observer.

Course topics (approximate):
Fundamental ideas of quantum mechanics. History of quantum mechanics. Double-slit experiment. Wave-particle duality. Wavefunctions. Time independent Schrödinger equation (TISE). Exact solutions of the TISE for simple problems. Particle in an infinitely deep potential well. Particle and an infinitely thick finite potential barrier. Particle in a finite potential well. Time dependent Schrödinger equation (TDSE). Probability current. Exact solutions of the TDSE for simple problems. Wavepackets. Heisenberg uncertainty principle. Wavefunction (state) space. Linear operators. Eigenvalue equation. Expectation value. Commutator. Special types of linear operators (Hermitian, unitary, inverse) and their properties. Examples of linear operators in quantum mechanics: Hamiltonian, momentum, position operators. Orthonormal basis of the state space. Dirac notation. Closure relation. Representations in the state space and change of representation. The postulates of quantum mechanics and applications. Formulation of the postulates: quantum state, observable, measurement, and the evolution of a quantum state. Commuting observables. Density operator and density matrix. Time evolution of the mean value of an observable. Evolution operator. The Schrödinger and Heisenberg pictures. General form of the uncertainty principle. Separable states. Entangled states. Single and two-qubit states; Bell states. Quantum key distribution, teleportation, superdense coding. Harmonic oscillator. Review of the classical harmonic oscillator. Quantum harmonic oscillator (QHO) – 1D case. Time evolution of the 1D QHO. Coherent states. Annihilation and creation operators. Approximation methods in quantum mechanics. Finite basis subsets. Time-independent nondegenerate perturbation theory. Time-independent degenerate perturbation theory. Variational method. Time-dependent perturbation theory and applications. Fermi's golden rule. Refractive index. Nonlinear optical coefficients. Methods for one-dimensional problems. Transfer matrix method. WKB method. Electron emission with a potential barrier. Quantum mechanics in crystalline materials. Bloch theorem. K.p method. Effective mass approximation. Density of states. Optical absorption. Angular momentum in quantum mechanics. Orbital angular momentum. Angular momentum operators and commutation relations. General theory of angular momentum in quantum mechanics. Eigenvalues and eigenstates of orbital angular momentum; spherical harmonics. Spin angular momentum. The hydrogen atom. Particle in a central potential. Solution of the hydrogen atom problem. Systems of identical particles. Identical particles in quantum vs. classical mechanics. Systems of two identical particles. Bosons and fermions. System of an arbitrary number of identical particles. Permutation operators; symmetrizer and antisymmetrizer. Symmetrization postulate and construction of physical states for systems of identical particles. Construction of basis for a system of identical particles. Differences between bosons and fermions. Pauli exclusion principle. Thermal distribution functions (Bose-Einstein and Fermi-Dirac). Direct and exchange terms. The consequences of particle indistinguishability: quantum interference; bunching, antibunching. Introductory quantum optics. Quantization of the electromagnetic field. Finite one-dimensional cavity case. Free space case. General approach (for lossless medium). Electric and magnetic field operators. Uncertainty principle for electric and magnetic fields in a mode. Multimode fields. Fock (number) states. Coherent states. Squeezed states. Quantum mechanics of fermions. Fermion annihilation and creation operators. Fermion wavefunction operator. Fermion Hamiltonians (for noninteracting particles). General form of a single-particle fermion operator. Hamiltonian for two interacting fermions. Interaction of different kinds of particles. Electron-photon interaction. Stimulated emission. Spontaneous emission. Optical absorption. Quantum computation. Interpretations of quantum mechanics.

Quantum Mechanics Visualization Applets

Applets include:
Hydrogen Atom Applet. Molecular Orbitals Applet. 1-D Quantum Mechanics Applet. 1-D Quantum Crystal Applet. 2-D Quantum Crystal Applet. 1-D Quantum Transitions Applet. Atomic Dipole Transitions Applet. 2-D Rectangular Square Well Applet. 2-D Circular Square Well Applet. 2-D Quantum Harmonic Oscillator Applet. Quantum Rigid Rotator Applet. 3-D Quantum Harmonic Oscillator Applet.

Classical Physics

7 lectures by Professor V. Balakrishnan, Department of Physics. IIT Madras

Video Course topics:
Introduction to classical mechanics. Short history. Basic concepts of force, motion, mass and units of physical quantities used in laws of motion. Description of motion in one dimension. Description of motion in two and three dimensions. Laws of motion. Work, energy and power. Circular motion. Uniform circular motion. Centripetal acceleration. Rotational motion. Gravitation. Oscillations. Waves.

Classical Mechanics

9 lectures by Leonard Susskind. Stanford University.

Course topics:
Lagrangian Formulation of Mechanics. Hamiltonian Formulation of Mechanics. Degrees of freedom and equations of motion. Conservation of Energy and Momentum. The Calculus of Variations. Euler-Lagrange equations. Constrained Systems and Lagrange multipliers. Oscillators. Small fluctuations. Damped, forced and anharmonic oscillations. One dimensional systems. Motion in a central field. Kepler's laws. Symmetries and Conservation laws. Noether's theorem. Gallilean relativity. Rotation. Euler's equations. Rigid Bodies. Theory of small fluctuations. Molecules. Hamiltonian Mechanics. Phase space. Poisson brackets. Canonical Transformations. Symmetries. Noether's theorem.

Oscillations and Waves

44 lectures by professor S.Bharadwaj, Department of Physics and Meteorology, IIT Kharagpur.

Course topics:
Simple Harmonic Oscillators. Damped Oscillator. Oscillator With External Forcing. Resonance. Coupled Oscillations. Sinesoidal Plane Waves. Electromagnetic waves. The Vector Nature of Electromagnetic Waves. The Electromagnetic Spectrum. Interference. Coherence. Diffraction. X-Ray Diffraction. Beats. The Wave Equation. Solving the Wave Equation. Waves. Standing Waves. Polarization. Compton Effect. Wave - Particle Duality. Probability Amplitude. Probability. Schrodinger Wave Equation. Measurements. Particle in a Potential. Potential Well. Quantum Tunneling.

Chaos, Fractals and Dynamical Systems

40 lectures by professor S.Banerjee, Department of Electrical Engineering, IIT Kharagpur.

Course topics:
Representations of Dynamical Systems. Vector Fields of Nonlinear Systems. Limit Cycles. The Lorenz Equation. The Rossler Equation and Forced Pendulum. The Chuas Circuit. Discrete Time Dynamical Systems. The Logistic Map and Period doubling. Flip and Tangent Bifurcations. Intermittency Transcritical and pitchfork. Two Dimensional Maps. Bifurcations in Two Dimensional Maps. Introduction to Fractals. Mandelbrot Sets and Julia Sets. The Space Where Fractals Live. Interactive Function Systems. IFS Algorithms. Fractal Image Compression. Stable and Unstable Manifolds. Boundary Crisis and Interior Crisis. Statistics of Chaotic Attractors. Matrix Times Circle: Ellipse. Lyapunov Exponent. Frequency Spectra of Orbits. Dynamics on a Torus. Analysis of Chaotic Time Series. Control of Chaos. Non-Smooth Bifurcations. Normal from for Piecewise Smooth 2D Maps. Multiple Attractor Bifurcation and Dangerous. Dynamics of Discontinuous Maps. Introduction to Floquet Theory. The Monodromy Matrix and the Saltation Matrix.

Linear Dynamical Systems

20 lectures at Stanford University. EE263.

Course topics:
Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.

Heat and Mass Transfer

35 lectures by professor S.P.Sukhatme and professor U.N.Gaitonde, Department of Mechanical Engineering, IIT Bombay.

Course topics:
Introduction on Heat and Mass Transfer. Heat Conduction. Thermal Radiation. Review Of Fluid Mechanics. Forced Convection. Natural Convection. Heat Exchangers. Boiling and Condensation. Introduction to Mass Transfer.

Einstein's Theory - General Relativity

9 video lectures by Leonard Susskind. Stanford University.

Course topics:
Gravitational and Newtonian Physics. Special Relativity. Special Relativistic Mechanics. Gravity as Geometry. Curved Spacetime. Geodesics. Geometry outside Spherical Star. Black Holes. Gravitational Waves. Tensor calculus. Einstein Equations. General Relativity. Tests of Einstein's theory of general relativity. Gravitational radiation. Action principle. Symmetric spaces. Cosmology.

Have fun with these and until next time!

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