Expectation values of operators
PROFESSOR: Expectation values of operators. So this is, in a sense, one of our first steps that we're going to take towards the interpretation of quantum mechanics. We've had already that the wave function tells you about probabilities. But that's not quite enough to have the full interpretation of what we're doing. So let's think of operators and expectation values that we can motivate. So for example, if you have a random variable q, that can take values-- so this could be a coin that can take values heads and tails. It could be a pair of dice that takes many values-- can take values in the set q1 up to qn with probabilities p1 up to pn, then in statistics, or 8044, you would say that this variable, this random variable has an expectation value. And the expectation value-- denoted by this angular symbols over here, left and right-- it's given by the sum over i, i equal 1 to n, of the possible values the random variable can take times the probabil...