This is the second in a series of youtube video's I am making. Which I have chosen to name “Quantum Theory in Plain Language”.
In this particular video I give what I hope is a simple and accurate explanation of Dirac's Bra-Ket Algebra. First I introduce the concept of the ket and bra as representing quantum states. (Which in the first video are defined as consisting of information describing a physical system.) Then I define what in the video I call a “ket space”. I make use of the average persons intuition from high school algebra or geometry. In particular the concept of the 2D (x,y) plain. Where the inner product <bra|ket> on the space is the simple dot product. Then I make the conceptual connection from that to the spins of electrons with the convex combination forming a ket space. Once that is done only at the end and as “extra credit” do I make mention of any calculus.
In the video to follow I plan on explaining as simply as possible the concept of an operator on a inner product space. I will term unitary operators as “evolutions” and hermitian operators as “observables”. I will also have to introduce the commutator. Which will allow me to discuss the uncertainty principle in concrete but simple terms that anyone with a quality 12th grade education should be able to understand.
In case the youtube embed code does not show up for some reason here is a plain old link. Quantum Theory: Lesson two Bra-Ket Algebra