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Time Dependent Quantum Chemistry

Prof. Atanu Bhattacharya · GITAM Visakhapatnam

Start with lecture 1 At NPTEL

About

In our current course curriculum, except for time-dependent perturbation theory, physical chemistry students are not introduced to the time dependent quantum chemistry at all. This creates a big knowledge gap in students working on chemical dynamics, spectroscopy, and ultrafast spectroscopy fields. Objective of this course is to fulfil the knowledge gap not only by introducing the subject to them, but also by helping them use numerical methods to practically deal with some selected time-dependent quantum chemistry problems.

Intended audience: Physics/Chemistry UG PG students

Prerequisites: Must have a fair idea of postulates of quantum mechanics (as given in Quantum Chemistry or Physical Chemistry book by McQuarrie).INDUSRTY SUPPORT: Industries where quantum theory is extensively used.INTENDED AUDIENCE: Physics/Chemistry UG PG students

Lectures

Week 1 - Module 1 (Introduction)

  1. Introduction to TDSE YouTube
  2. Solution to TDSE, Stationary and Non-stationary States YouTube
  3. Electron and Vibrational Superposition States YouTube
  4. Optical Analogy to Quantum Superposition YouTube
  5. Introdution to Python Programming YouTube
  6. Simple Computation with Python Programming YouTube
  7. Plotting Graph with Python Programming YouTube

Week 2 Module 2 (Quantum-Classical Correspondence)

  1. Meaning of Probability Density YouTube
  2. Time Evolution of Normalization Constant YouTube
  3. Expectation Value and its Time Evolution YouTube
  4. Equation of Continuity YouTube
  5. Bohmian Mechanics YouTube
  6. Bohmian Mechanics and Standard Interpretation YouTube
  7. Grid Representation of Wavefunction YouTube
  8. Normalizing the Discretized Wavefunction and Finding Expectation Value YouTube

Week 3 Module 3 (Translational Motion)

  1. Plane Matter Wave and Wavepacket YouTube
  2. Wavepacket YouTube
  3. Stationary Gaussian Wavepacket YouTube
  4. Travelling Gaussian Wavepacket YouTube
  5. General Form of the Gaussian Wavepacket YouTube
  6. Fourer Transform of a wavefunction YouTube
  7. x-grid to k-grid YouTube
  8. Fourier Transform using fft YouTube

Week 4 Module 4 (Quantum Mechanics and Linear Algebra)

  1. Hilbert Space and Its Properties YouTube
  2. Basis Set Approach to Quantum Mechanics YouTube
  3. Matrix Algebra YouTube
  4. Eigenvalue and Eigenfunction YouTube
  5. Matrix Representation of Operators YouTube
  6. Matrix Representation of Hamiltonian Operator YouTube
  7. Diagonalizing Matrix YouTube
  8. Diagonalizing Tridiagonal Matrix YouTube

Week 5 Module 5 (Numerical Solution to TDSE)

  1. Time Evolution Operator YouTube
  2. Split Operator Metho YouTube
  3. Numerical Implementation of Split Operator Method YouTube
  4. Wavepacket Dynamics under zero interaction potential YouTube
  5. Wavepacket Dynamics under zero interaction potential continued YouTube
  6. Wavepacket Dynamics under linear interaction potential YouTube

Week 6 Module 6 (Adiabatic Theory)

  1. Quantum Adiabatic Theory YouTube
  2. Formal Derivation of Quantum Adiabatic Theory YouTube
  3. Geometric Phase and Dynamical Phase YouTube

Week 7 Module 7 (Nonradiative Transition) Part 1

  1. Nonradiative Transition part 1 YouTube
  2. Nonradiative Transition part 2 YouTube
  3. Nonradiative Transition part 3 YouTube

Week 8 Module 8 (Nonradiative Transition)Part2

  1. Quantum Dissipative Dynamics YouTube
  2. Quantum Dissipative Dynamics cont YouTube
  3. Formal Derivation of Dissipative Quantum Dynamics YouTube

Week 9 Module 8 (Light-Atom Interaction), Part 1

  1. Classical Description of Light YouTube
  2. Vector and Scalar Potential YouTube
  3. Vector and Scalar Potential YouTube

Week 10 Module 8 (Light-Atom Interaction), Part 2

  1. Master Equation of Light YouTube
  2. Hamiltonian for Light-Atom Interaction YouTube
  3. Hamiltonian for Light-Atom Interaction YouTube

Week 11 Module 8 (Light-Atom Interaction), Session 5

  1. Absorption and Stimulated Emission YouTube
  2. Absorption and Stimulated Emission YouTube

Week 12 Module 9 (Time Domain Appraoch to Spectroscopy), Session 1

  1. Time Correlation Function YouTube
  2. Fourier Transform of Time Correlation Function YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
GITAM Visakhapatnam
Department
Chemistry and Biochemistry
Teacher
Prof. Atanu Bhattacharya
Level
Graduate
Language
English
Subjects
Chemistry
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IISc Bangalore.
Who can watch
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