Heisenberg Uncertainty Principle and compatible operators
The Schrödinger and Heisenberg pictures of quantum mechanics
Coherent and Squeezed States
Two state systems and applications to NMR and MRI
This physics course covers Heisenberg’s uncertainty principle and the concept of compatible operators. You will also learn about the Schrödinger and Heisenberg pictures of quantum mechanics and the coherent and squeezed states of the harmonic oscillator. The course concludes with two state systems and their applications to NMR and masers.
This is the second of three courses offering a sophisticated view of quantum mechanics and its proper mathematical foundation.
Part 1: Wave Mechanics
Part 2: Quantum Dynamics
Part 3: Entanglement and Angular Momentum
To understand the material in this course you should have taken Mastering Quantum Mechanics Part 1: Wave Mechanics.
Completing the 3-part Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics
The series will follow MIT’s on campus 8.05, the second semester of the three-course sequence on undergraduate quantum mechanics, and will be equally rigorous. 8.05 is a signature course in MIT’s physics program and a keystone in the education of physics majors.
“I’ve thought long and hard to come up with a better MOOC than this one (I’ve completed 25 of these things over the past 2 years) and can’t do it. 8.05x is #1 and I suspect will stay that way for some time to come.”
“Being an engineering student from India trying to shift to Physics, I am often faced with the requirement to study topics on my own. Very often this has led me to feel inadequate. 8.05x was the perfect opportunity for me to both gain knowledge and evaluate my understanding on a high quality international platform. It has really exceeded my expectations. Now, at the end of fifteen weeks, I feel more confident and hopefully I am more knowledgeable.”
Week 1: The uncertainty principle and compatible operators.
Week 2: The harmonic oscillator, Schrodinger equation as unitary time evolution, The Heisenberg picture of quantum mechanics.
Week 3: Coherent and squeezed states of the harmonic oscillator.
Week 4: Coherent photon states. Two state systems, Nuclear Magnetic Resonance (NMR), and the ammonia maser.
Week 5: The setup for NMR (Nuclear Magnetic Resonance) and basic MRI (Magnetic Resonance Imaging).