Introduction

Until this point in the course, we have always started with physical laws that you learned in your earlier courses on mechanics and electricity and magnetism and worked carefully, step by step through their consequences. Now, we shall use the framework which we have built to describe waves to reveal new physical laws for systems which you have not yet studied. The result will be the laws of quantum mechanics.

Quantum mechanics is a fascinating subject. It teaches that much of what you accept as common sense is wrong and that most everything you have learned so far in physics is not correct. The following three statements summarize the main intellectual content of quantum mechanics.

• Anything can happen (almost¹).

  It is entirely possible for a person to run towards a wall -- even without enough energy to break through it -- and end up on the other side. A ball thrown perfectly straight through a door -- even in vacuum so that there is nothing to deflect it -- can take a sharp turn to the upon exiting the door. The moon could suddenly appear on the other side of its orbit from where you calculate it should be using Newton's laws. None of these things violates the laws of physics; all have a non-zero probability of happening. The world is indeed a magical place.

• No one can say what will happen.

  In addition to all sorts of unexpected things being possible, the world is also quite mysterious. It is impossible under the laws of physics ever to predict what will happen.

• We can give the probabilities of the different possibilities.

  Without this, there would be very little more to say, and physics would be a truly useless subject. It turns out that even with all of this unpredictability it is possible to determine the chances of different things happening. The subject of quantum mechanics consists mostly of learning to compute these probabilities and understanding what they mean for the world around us.