# Lecture 6 | Modern Physics: Quantum Mechanics (Stanford) | Summary and Q&A

## Summary

In this video, the instructor discusses the concept of polarization in quantum mechanics. He explains how the polarization of a photon can be described by a vector, and how it can be measured using polarizers. The video also explores the properties of polarization vectors and how they relate to classical wave behavior. Additionally, the instructor introduces the concept of observables and their eigenvalues and eigenvectors in the context of photon polarization.

## Questions & Answers

### Q: What is the simplest system for studying the difference between classical and quantum thinking?

The polarization of a photon is considered the simplest system for studying the difference between classical and quantum thinking.

### Q: How can the polarization of a photon be visualized?

The polarization of a photon can be visualized as a flag perpendicular to the motion of the photon in a plane perpendicular to the motion.

### Q: What happens when a photon passes through a polarizer?

When a photon passes through a polarizer, it becomes polarized in the direction of the polarizer's axis.

### Q: How can the polarization of a photon be measured?

The polarization of a photon can be measured by sending it through a polarizer and observing whether it passes through or not.

### Q: What is the significance of symmetry in analyzing photon polarization?

The symmetry of rotation in the XY plane allows for the construction of polarizers pointing at any angle, resulting in different polarization outcomes for the photon.

### Q: What are the mathematical representations of polarization states?

The X polarization state can be represented by the vector [1, 0] or as the state labeled X. The Y polarization state can be represented by the vector [0, 1] or as the state labeled Y.

### Q: What is an observable and how is it related to polarization?

An observable is a quantity that can be measured or detected in an experiment. In the context of polarization, the observable is associated with the polarization direction and its measurements correspond to definite outcomes.

### Q: How can the observable linked to polarization be represented mathematically?

The observable associated with polarization in the XY plane can be represented by the matrix [1 -1] when it acts on the X polarization state. Similarly, it can be represented by the matrix [0 1] when it acts on the Y polarization state.

### Q: What is the physical significance of orthogonal polarization states?

Orthogonal polarization states represent mutually exclusive outcomes of an experiment and are used to determine probabilities of specific polarization directions.

### Q: How can the probability of a photon passing through a polarizer be calculated for an arbitrary angle?

The probability of a photon passing through a polarizer at an arbitrary angle can be calculated by taking the inner product (or dot product) between the initial polarization state and the polarization state associated with the polarizer, and squaring the result.

## Takeaways

In this video, we learned about polarization in quantum mechanics and how it can be analyzed using polarizers. We saw that the polarization of a photon can be represented by vectors, and that different polarizers can produce different polarization outcomes. We also saw the importance of symmetry and observed how observables are related to polarization measurements. Overall, polarization provides a simple system for studying quantum mechanics and highlights the differences between classical and quantum thinking.