Brief Introduction
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.
Description
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 Schrodinger 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.
After completing 8.04x, you will be ready to tackle the Mastering Quantum Mechanics course on edX, which will be available in Spring 2021.
Knowledge
- 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
- Three-dimensional central potentials
- Solution of the hydrogen atom
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