# Chapter 2

# Entering the Matrix: Welcome to State Vectors

In This Chapter

- Creating state vectors
- Using Dirac notation for state vectors
- Working with bras and kets
- Understanding matrix mechanics
- Getting to wave mechanics

Quantum physics isn't just about playing around with your particle accelerator while trying not to destroy the universe. Sometimes, you get to do things that are a little more mundane, like turn lights off and on, perform a bit of calculus, or play with dice.

If you're actually doing physics with those dice (beyond hurling them across the room), the lab director won't even get mad at you. In quantum physics, absolute measurements are replaced by probabilities, so you may use dice to calculate the probabilities that various numbers will come up. You can then assemble those values into a vector (single-column matrix) in Hilbert space (a type of infinitely dimensional vector space with some properties that are especially valuable in quantum physics).

This chapter introduces how you deal with probabilities in quantum physics, starting by viewing the various possible states a particle can occupy as a vector — a vector of probability states. From there, I help you familiarize yourself with some mathematical notations common in quantum physics, including bras, kets, matrices, and wave functions. Along the way, you also get to work with some important operators.

## Creating Your Own Vectors in Hilbert Space

In quantum physics, probabilities take the place of absolute measurements. ...