Learn · Introductory Quantum Mechanics
Lecture 47 of 55Week 7
Angular momentum operator and its eigenfunctions
Prof. Manoj Harbola · IIT Kanpur
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All the lectures
- Black Body Radiation I - Relevant Definitions and Black Body as cavity
- Black Body Radiation II- Intensity of radiation in terms of energy density
- Black Body Radiation III - Spectral energy density and radiation pressure inside a black body radiation
- Black Body Radiation IV- Stephen's Boltzman law
- Black Body Radiation V - Wein's Displacement law and analysis for spectral density
- Black Body Radiation VI - Wein's distribution law and rayleigh - Jeans distribution law
- Black Body Radiation VII - Quantum Hypothesis and plank's distribution Formula
- Radiation as a collection of particles called photons
- Quantum Hypothesis and specific heat of soilds
- Bohr's Model of hydrogen spectrum
- Wilson Sommerfeld quantum condition I - Harmonic oscillator and particle in a box
- Wilson Sommerfeld quantum condition II - Particle moving in a coulomb potential in a plane and related quantum numbers
- Wilson Sommerfeld quantum condition III - Particle moving in a coulomb potential in 3D and related quantum numbers
- Quantum conditions and atomic structure, electron spin and Pauli exclusion principle
- Interaction of atoms with radiation : Eienstien's A and B coefficients
- Stimulated emmision and amplification of light in a LASER
- Brief description of a LASER
- Introduction to the correspondence principle
- General nature of the correspondence principle
- Selection rules (for transitions) through the correspondence principle
- Applications of the correspondence principle : Einstiens A coefficient for the harmonic oscillator and the selection rules for atomic transitions
- Heisenberg's formulations of quantum mechanics : expressing kinetic variables as matrices
- Heisenberg's formulation of quantum mechanics : the quantum condition
- Heisenberg's formulation of the quantum mechanics : Application to harmonic oscillator
- Brief introduction to matrix mechanics and the quantum condition in matrix form
- Introduction to waves and wave equation
- Sationary waves eigen values and eigen functions
- Matter waves and their experimental detection
- Represenating a moving paticle by a wave packet
- Stationary-state Schrodinger equation and its solution for a particle in a box
- Solution of the stationary-state Schrodinger equation for a simple harmonic oscillator
- Equivalance of Heisenberg and the Schrodinger formulations : Mathematical preliminaries
- Equivalance of Heisenberg and Schrodinger formulations : The x and p operators and the quantum condition
- Born interpretation of the wavefunction and expectation values of x and p operators
- Uncertainty principle and its simple applications
- Time dependent Schrodinger equation the probability current density and the continuity equation for the probability density
- Ehrenfest theorem for the expectation values of x and p operators
- Solution of Schrodinger equation for a particle in one and two delta function potentials
- Solution of Schrodinger equation for a particle in a finite well
- Numerical solution of a one dimensional Schrodinger equation for bound states - I
- Numerical solution of a one dimensional Schrodinger equation for bound states - II
- Reflection and transmission of particles across a potential barrier
- Quantum-tunneling and its examples
- Solution of the Schrodinger for free paticles and periodic boundary conditions
- Electrons in a metal : Density of states and Fermi energy
- Schrodinger equation for particles in spherically symmetric potential, angular momentum operator
- Angular momentum operator and its eigenfunctions
- Equation for radial component of the wavefunction in spherically symmteric potentials and general properties of its solution
- Solution for radial component of the wavefunction for the hydrogen atom
- Numerical solution for the radial component of wavefunction for spherically symmetric potentials
- Solution of the Schrodinger equation for one dimensional periodic potential : Bloch's theorem
- Kroning-Penny model and energy bands
- Kroning-Penny model with periodic Dirac delta function and energy bands
- Discussion on bands
- Summary of the course