A course that develops the tools and the mathematical foundation needed to have a working knowledge of Quantum Mechanics.
The course offers a sophisticated view of quantum mechanics and its proper mathematical foundation. It will give you the tools needed to do research in quantum mechanics and to understand many current developments.
8.05 is the second semester of the three-course sequence on undergraduate quantum mechanics at MIT. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors. The online course 8.05x will follow the on-campus version and will be equally rigorous.
To master this material and to follow the course, you will likely need a time investment of ten to twelve hours a week. There will be weekly homework, one mid-term test, and a final exam.
Review of wave mechanics. Variational principle. Spin operators and general spin one-half states. Elements of linear algebra: complex vector spaces and linear operators. Hermitian operators and unitary operators. Dirac bra-ket notation. The uncertainty principle and compatible operators.
Schrodinger equation as unitary time evolution. The Heisenberg picture of quantum mechanics. Coherent and squeezed states of the harmonic oscillator. Two-state systems. Nuclear magnetic resonance and the ammonia maser.
Multiparticle states and tensor products. Entanglement and quantum teleportation. The Einstein, Podolsky, Rosen paradox and Bell inequalities. Identical particles: bosons and fermions.
Angular momentum and central potentials. Representations of angular momentum. Hidden symmetries and degeneracies. Addition of angular momentum. Algebraic solution of the hydrogen atom.
Modern engineering research focuses on designing new materials and processes at the molecular level. Statistical thermodynamics provides the formalism for understanding how molecular interactions lead to the observed collective behavior at the macroscale. This course will develop a molecular-level understanding of key thermodynamic quantities like heat, work, free energy and entropy. These concepts will be applied in understanding several important engineering and biological applications.
General relativity and quantum mechanics are the most successful theories in science. But at least one is wrong. Imperial's Michael Duff outlines why M-theory is our only candidate for an ultimate theory.
Chemical reactions underpin the production of pretty much everything in our modern world. But, what is the driving force behind reactions? Why do some reactions occur over geological time scales whilst others are so fast that we need femtosecond-pulsed lasers to study them? Ultimately, what is going on at the atomic level? Discover the answers to such fundamental questions and more on this course in introductory physical chemistry.