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Computational spectroscopy and computational quantum chemical dynamics is a vast field in physical chemistry. Significant part of this field is developed based on the concepts of time-dependent quantum mechanics and its numerical implementations. This book gives an introduction to the Time-Dependent Quantum Chemistry for use with any introductory college/university course in optics, spectroscopy, kinetics, dynamics, or experimental physical chemistry or chemical physics of the kind usually taken by undergraduate and graduate students in physical chemistry. In this book, different concepts of time-dependent quantum mechanics are systematically presented by first giving emphasis on the contrasting viewpoint of classical and quantum mechanical motion of a particle, then by demonstrating the ways to find classical flavour in quantum dynamics, thereafter by formally defining the wavepacket which represents a quantum particle and finally by demonstrating numerical methods to explore the wavepacket dynamics in one dimension. Along with the analytical theory, accompanying Python chapters in this book take readers to a hands-on tour with Python programming by first giving them a quick introduction to the Python programming, then by introducing the position-space grid representation of the wavefunction, thereafter, by making them familiarized with the Fourier transform to represent the discretized wavefunction in momentum space, subsequently by showing the Python-based methodologies to express Hamiltonian operator in matrix form and finally by demonstrating the entire Python program which solves the wavepacket dynamics in one dimension under influence of time-independent Hamiltonian following split-operator approach. Rigorous class-testing of the presented lecture notes at the Indian Institute of Science, GITAM University and at NPTEL platform reveals that physical chemistry students, after thoroughly going through all chapters, not only develop an in-depth understanding of the wavepacket dynamics and its numerical implementations, but also start successfully writing their own Python code for solving any one dimensional wavepacket dynamics problem.
For this textbook, the Python programming language is selected due to many favorable reasons: It is very easy to learn, it is becoming increasingly popular within the modern scientific community for its rich scientific libraries, and it is freely available.
Along with the above chapters, where students realize the theory of wavepacket dynamics in one dimension thoroughly, accompanying five PythonChapters (from A to E) take them on a hands-on tour with Python programming so that they can finally solve one-dimensional wavepacket dynamics numerically. Giving a thorough hands-on experience, even with the simplest quantum dynamics problem, to students with no prior experience with programming or numerical methods is a very tricky task. This, however, has been accomplished here by first giving them a quick introduction to Python programming (in PythonChapter A), then by introducing the position-space grid representation of the wavefunction (in PythonChapter B), thereafter by making them familiarized with Fourier transforms to represent discretized wavefunctions in momentum space (numerical method of implementing the time propagator requires a wavefunction to be represented in momentum space: a concept which is developed in Chapter 5), subsequently by showing the Python-based methodologies to express the Hamiltonian operator in matrix form (in PythonChapter D), and finally by demonstrating an entire Python program which solves the wavepacket dynamics in one dimension under the influence of a time-independent Hamiltonian following the split-operator approach (in PythonChapter E). To reach the final goal of exploring wavepacket dynamics in one dimension, as discussed in PythonChapter E, one has to systematically go through the material given in PythonChapters A–D.
Preface
Introduction
Introduction to Quantum Dynamics with Quantum Superposition
Introduction to Quantum Dynamics with a Classical Mechanical Flavor
Time-Dependent Quantum Mechanics of Translational Motion
Quantum Mechanics from a Linear Algebra Viewpoint
Numerical Solution to the TDSE
Application of Wavepacket Dynamics: Illuminating Examples
Appendix I. Multiple Choice Questions