Coming soon
QUANTUM MECHANICS
Course Objectives:
This course will enable the students to –
- Understand the limitations of classical mechanics and the need of quantum chemistry, apply the postulates of quantum mechanics to solve various systems.
Course Outcomes (COs):
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Course Outcomes
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Teaching, Learning Strategies |
Assessment Strategies |
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On completion of this course, the students will be able to – CO91: develop an understanding of quantum mechanical operators, concepts of quantization, wave function and postulates of quantum mechanics. CO92: normalize simple wave function and calculate average physical property for a system like energy, momentum etc. CO93: describe quantization of translational, vibrational and rotational energy levels and wave function of respective energy state. CO94: solve Schrodinger wave equation for the hydrogen atom and discuss the concepts of quantum numbers. CO95: apply the quantum mechanical approach for chemical bonding theories. |
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Black-body radiation, Planck’s radiation law, photoelectric effect, Bohr’s model of hydrogen atom (no derivation) and its defects, Compton effect, de Broglie hypothesis, Heisenberg’s uncertainty principle, heat capacity of solids.
Sinusoidal wave equation, operators, Hamiltonian operator, eigen function, eigen values, Schrodinger wave equation and its importance, physical interpretation of the wave function, postulates of quantum mechanics.
Application of Schrodinger equation to free particle and particle in a one dimensional box (rigorous treatment), quantization of energy levels, zero-point energy and justification for Heisenberg Uncertainty principle, extension to three dimensional box, concept of degeneracy.
Vibrational motion- simple harmonic oscillator model of vibrational motion, classical treatment, quantum mechanical treatment, interpretation of the results of Schrödinger wave equation, comparison of classical and quantum mechanical results.
Rotational motion- coordinate systems, cartesian and spherical polar coordinates and their relationships. Schrodinger wave equation in spherical polar coordinates for rigid rotator model, separation of variables, the phi and the theta equations and their solutions, Legendre and associated Legendre polynomials, spherical harmonics (imaginary and real forms), polar diagrams of spherical harmonics.
Schrodinger wave equation for H-atom, separation into three equations, qualitative treatment of hydrogen atom, quantum numbers and their importance, radial distribution functions of 1s, 2s, 2p, 3s, 3p and 3d orbitals and polar plots of their shapes, selection rules and spectra of Hydrogen atom.
Concept of s, s*, p, p* orbitals and their characteristics, introduction to valence bond model of H2, molecular orbital theory, basic ideas of forming M.O.’s from A.O.’s, construction of M.O’s by LCAO (H2+ ion and H2), calculation of energy levels from wave functions, physical picture of bonding and antibonding wave functions, comparison of LCAO-MO and VB treatments of H2, hybrid orbitals – sp, sp2, sp3, calculation of coefficients of A.O.’s used in these hybrid orbitals.
- Quantum Chemistry, Fourth Revised Edition; R.K. Prasad; New Age International (P) Ltd Publishers, New Delhi, 2020
SUGGESTED READINGS:
- Introductory Quantum Chemistry, Fourth Edition; A. K. Chandra; Tata McGraw-Hill, 2017.
- Quantum Chemistry, Seventh Edition; Ira N. Levine; Pearson Education India, New Delhi, 2014.
- Molecular Quantum Mechanics, Fifth Edition; P.W. Atkins, and R.S. Friedman; Oxford University Press Club, New York, 2012.
- A Textbook of Physical Chemistry, Quantum Chemistry and Molecular Spectroscopy, Vol. IV, Sixth Edition; K. L. Kapoor; McGraw Hill Education Private Limited, 2020.
e-RESOURCES:
- Mod-01 Lec-01 Quantum Mechanics -- An Introduction – YouTube
- https://www.youtube.com/watch?app=desktop&v=pGerRhxNQJE
- https://nptel.ac.in/courses/115101107
