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December 15, 2022


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This course presents an introduction to quantum mechanics.

It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems — the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy.


The material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW was prepared in the early 1990’s by Prof. Sylvia T. Ceyer. These were revised and transcribed to electronic form primarily by Prof. Keith A. Nelson. The current version includes additional contributions by Professors Moungi G. Bawendi, Robert W. Field, Robert G. Griffin, Robert J. Silbey and John S. Waugh, all of whom have taught the course in the recent past.

Course Curriculum

  • Historical development Unlimited
  • The atom of Niels Bohr Unlimited
  • Wave nature, de Broglie wavelength Unlimited
  • Uncertainty principle Unlimited
  • Stationary waves, Schrödinger equation Unlimited
  • Particle in a box Unlimited
  • Probabilities, expectation values, operators I Unlimited
  • Probabilities, expectation values, operators II Unlimited
  • Postulates of quantum mechanics I Unlimited
  • Postulates of quantum mechanics II Unlimited
  • Classic harmonic oscillator Unlimited
  • Quantum harmonic oscillator Unlimited
  • Tunneling Unlimited
  • Three dimensional systems Unlimited
  • Spherical harmonics Unlimited
  • Angular momenta Unlimited
  • Hydrogen atom I Unlimited
  • Hydrogen atom II Unlimited
  • Variation principle Unlimited
  • Helium atom Unlimited
  • Electron spin Unlimited
  • Pauli principle Unlimited
  • Born-Oppenheimer approximation Unlimited
  • Molecular orbital theory, H2+ Unlimited
  • LCAO-MO theory Unlimited
  • Qualitative molecular orbital theory Unlimited
  • Interaction of light with matter Unlimited
  • Vibrational spectra Unlimited
  • NMR spectroscopy I Unlimited
  • Perturbation theory Unlimited
  • Vibrational anharmonicity Unlimited
  • Crystal field states Unlimited

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Massachusetts Institute of Technology