- The Electron Double-Slit Experiment
- Lectures on Quantum Mechanics
- Computational Quantum Mechanics: Solving Schrodinger Equation
- The Quantum Harmonic Oscillator: Eigenvalues and Eigenfunctions
- Time Evolution of Quantum States: The ‘Kicked’ Harmonic Oscillator
- Time Evolution: Scattering off a Square Well
- The Morse Potential and the Diatomic Molecule
- Application to an Undergraduate Laboratory Experiment: The Iodine Vapor Experiment
The Electron Double-Slit Experiment
The famous thought Experiment discussed in Feynman Lectures Vol.3 realized through an ‘Electron Biprism’ setup by Hitachi (https://www.hitachi.com/rd/research/materials/quantum/doubleslit/index.html). The ‘double-slit’ is formed through an electrostatic biprism formed two parallel plates and a thin filament (about a micron) at the center. The filament is kept at a positive potential and the plates grounded. The resulting setup acts as a biprism for electrons. Single electrons are observed on the screen, striking one at a time in a seemingly random pattern. However, as time passed, a clear interference pattern emerges
Lectures on Quantum Mechanics
Lectures I gave till a few years back. I have excluded path integrals, which I used to discuss in my first few years of teaching. Eventually, I decided to start more traditionally, with electron spin.
Master-1Computational Quantum Mechanics: Solving Schrodinger Equation
I use simple discretisation, since it reduces every thing to matrix form, making contact with N-state systems.
Schrodinger_EquationThe Quantum Harmonic Oscillator: Eigenvalues and Eigenfunctions
Time Evolution of Quantum States: The ‘kicked’ Harmonic oscillator
The animation generated for the ‘kicked’ harmonic oscillator
Time Evolution: Scattering off a square well
Animation for scattering off a square well
The Morse Potential and the Diatomic Molecule
The Morse Potential is a phenomenological potential energy describing the interaction between the two atoms of a homo-polar molecule. Following is the form of the potential energy function
The following jupyter notebook discusses the theory and context and generates the energy states for molecular vibrations
Application to an undergraduate Laboratory Experiment: The Iodine Vapor Spectrum
The absorption spectrum of hot iodine vapor shows bands, each band generated due to transitions of the molecule from the electronic ground state to the electronic excited state. The potential energy function of each electronic state can be modeled as a Morse Potential, each with its own set of parameters. The absorption bands arise due to transitions from a vibrational state of the electronic ground state to a vibrational state of the electronic first excited state
There is an undergraduate lab experiment which analyzes the trends in the absorption bands to determine dissociation energy, anharmonicity, etc. The following jupyter notebook simulates the vibrational states for the electronic ground and excited state potentials. Comparison with the lab experiment allows determination of parameters