Quantum Mechanics: A First Course
Learn about wavefunctions and their probabilistic interpretation, how to solve the Schrödinger equation for a particle moving in one-dimensional potentials, scattering, central potentials, and the hydrogen atom.
start date
October 13, 2022
length
17 Weeks
effort
10-15 Hours/Week
price
Free
About this course
In this quantum physics course, you will learn the basics of quantum mechanics. We begin with de Broglie waves, the wavefunction, and its probability interpretation. We then introduce the Schrodinger equation, inner products, and Hermitian operators. We also study the time-evolution of wave-packets, Ehrenfest’s theorem, and uncertainty relations.
Next we return to the Schrödinger equation, solving it for important classes of one-dimensional potentials. We study the associated energy eigenstates and bound states. The harmonic oscillator is solved using the differential equation as well as algebraically, using creation and annihilation operators. We discuss barrier penetration and the Ramsauer-Townsend effect.
Finally, you will learn the basic concepts of scattering – phase-shifts, time delays, Levinson’s theorem, and resonances – in the simple context of one-dimensional problems. We then turn to the study of angular momentum and the motion of particles in three-dimensional central potentials. We learn about the radial equation and study the case of the hydrogen atom in detail.
This course is based on MIT 8.04: Quantum Mechanics I. At MIT, 8.04 is the first of a three-course sequence in Quantum Mechanics, a cornerstone in the education of physics majors that prepares them for advanced and specialized studies in any field related to quantum physics.
In this quantum physics course you will learn the basics of quantum mechanics. We begin with de Broglie waves, the wavefunction, and its probability interpretation. We then introduce the Schrodinger equation, inner products, and Hermitian operators. We also study the time-evolution of wave-packets, Ehrenfest’s theorem, and uncertainty relations.
Next we return to the Schrödinger equation, solving it for important classes of one-dimensional potentials. We study the associated energy eigenstates and bound states. The harmonic oscillator is solved using the differential equation as well as algebraically, using creation and annihilation operators. We discuss barrier penetration and the Ramsauer-Townsend effect.
Finally, you will learn the basic concepts of scattering – phase-shifts, time delays, Levinson’s theorem, and resonances – in the simple context of one-dimensional problems. We then turn to the study of angular momentum and the motion of particles in three-dimensional central potentials. We learn about the radial equation and study the case of the hydrogen atom in detail.
This course is based on MIT 8.04: Quantum Mechanics I. At MIT, 8.04 is the first of a three-course sequence in Quantum Mechanics, a cornerstone in the education of physics majors that prepares them for advanced and specialized studies in any field related to quantum physics.
What you’ll learn
- The wavefunction and its probability interpretation.
- Time-evolution of wave-packets.
- Ehrenfest’s theorem and uncertainty relations.
- Solutions of the Schrodinger equation for one-dimensional potentials: the square well and the harmonic oscillator.
- Barrier penetration and the Ramsauer-Townsend effect.
- Basics of quantum scattering in one dimension.
- Phase-shifts, time delay, Levinson’s theorem, and resonances.
- Angular momentum in Quantum Mechanics.
Prerequisites
Mathematics: Calculus and differential equations. Physics: introductory physics at the college level: mechanics, electromagnetism and waves
Meet your instructors
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Barton Zwiebach
Barton Zwiebach is presently Professor of Physics at the MIT Department of Physics. Zwiebach was born in Lima, Peru. His undergraduate work was done in Peru, where he obtained a degree in Electrical Engineering from the Universidad Nacional de Ingenieria in 1977.
His graduate work was in Physics, at the California Institute of Technology. Zwiebach obtained his Ph.D. in 1983, working under the supervision of Murray Gell-Mann. He has held postdoctoral positions at the University of California, Berkeley, and at MIT, where he became an Assistant Professor of Physics in 1987, and a permanent member of the faculty in 1994.
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Jolyon Bloomfield
Jolyon Bloomfield is a former Lecturer in Physics at MIT. He specialized in general relativity and cosmology research, with an interest in modified theories of gravity, particularly with an eye to explanations of dark energy. He has also made numerous contributions to the development of Open edX.