Mastering Quantum Mechanics
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Program Overview
Mastering Quantum Mechanics
The Mastering Quantum Mechanics course offers a sophisticated view of quantum mechanics and its proper mathematical foundation. Completing the course will give students the tools needed to do research in quantum mechanics and to understand many current developments.
About the Course
The course is divided into three parts. The first part reviews the basics of wave mechanics and introduces the variational principle. It then moves on to develop the technology of spin one-half states and spin operators. The last part of the module gives an in-depth look into linear algebra to establish the mathematical foundation necessary to do quantum mechanics. The module concludes by developing the bra-ket notation of Dirac.
The second part covers Heisenberg’s uncertainty principle and the concept of compatible operators. It continues to develop the Heisenberg and the Schrödinger pictures of quantum mechanics. The module also covers the coherent and squeezed states of the harmonic oscillator. It concludes with two state systems and their applications to NMR and masers.
The third part introduces the concept of tensor product states to discuss entanglement and Bell inequalities. The module also covers angular momentum and the representations of angular momentum. This is used to understand the spectrum of central potentials and to introduce hidden symmetries. It concludes with the subject of addition of angular momentum and an algebraic approach to the hydrogen atom spectrum.
Prerequisites
- Some knowledge of wave mechanics at the level of an introductory undergraduate course, 8.04x.
- Proficiency in calculus and some knowledge of linear algebra.
What You'll Learn
- Spin one-half and Spin Operators
- Vector spaces and linear operators
- Dirac’s Bra-ket notation
- Uncertainty Principle and compatible operators
- The Schrodinger and Heisenberg pictures of quantum mechanics. Axioms of quantum mechanics
- Coherent States. Two state systems and applications to NMR
- Entanglement and Bell’s inequality. Teleportation. No cloning
- Angular momentum and central potentials. Addition of angular momentum
- Density matrices and decoherence.
Instructors
- Barton Zwiebach, Professor of Physics
Time Commitment
Completing the course requires a time investment of at least 12 hours a week.
Duration
The course is estimated to last 18 weeks.
Tuition
The course is free to learn.
Who Can Take This Course
Because of U.S. Office of Foreign Assets Control (OFAC) restrictions and other U.S. federal regulations, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba, Syria, North Korea, and the Crimea, Donetsk People's Republic, and Luhansk People's Republic regions of Ukraine.