1. Nov 20, 2015

### alexis12

I'm an undergraduate in Physics and just cracked open some QM books, some seem to start with polarization and a strange way of introducing operators, while others start with the wavefunction and then go into harmonic oscilators, then the hydrogen atom etc..

What does polarization have to do with QM?

2. Nov 20, 2015

### bapowell

The polarization of light is associated with the spin of the photon. Textbooks that start off discussing polarization are probably using it to motivate the fact that particles have discrete angular momentum degrees of freedom and that only one polarization (or spin) axis can be measured at a time. These two facts combine to yield some puzzling outcomes. Suppose that light is sent through an x-axis polarizer so that all comes out either +x or -x polarized. Say we then block the -x polarization and let the remaining light pass through another x-axis polarizer. What comes out the other end? Unsurprisingly, +x polarized light. It gets spooky when you place a third polarizer oriented along a different axis in between these two. Suppose this third one is a z-axis polarizer, so you've got x, z, x polarizers. Like last time, you block the -x coming out of the first. What comes out of the final polarizer? Both +x and -x. This is the essence of the nuttiness of quantum measurement: the intervening z-axis polarizer acts to "reset" the system.

You may have heard of the Stern-Gerlach experiment: it's the analogous setting for electrons and some books start with that.

It also happens to a be nice way to get students comfortable with bra-ket notation, understanding superposition of states, and learning about angular momentum operators.

3. Nov 21, 2015

### forcefield

A single photon goes through a certain type of polarizer (tourmaline crystal) either completely or not at all. A classical wave would not behave that way.

4. Nov 21, 2015