# About this course

Skip About this courseThis 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.

**Learner Testimonials**

“*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.*”

### At a glance

# What you'll learn

Skip What you'll learn- 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

# Syllabus

Skip Syllabus**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).

**Final assessment**

# Learner testimonials

Skip Learner testimonials“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.”