Operator is the mapping from function set to function set, which acts on one function to make it become another function. There is a point on P that is the momentum operator, and point X is the coordinate operator. The exchange of two operators means that two operators act on a function successively, and then subtract after the order of the operators is exchanged. For example, the commutators of two operators P and Q are P (q (f (x))-Q (p (f (x)). I don't know what means, < x | p > means the inner product of two state vectors, | p > means the state vector, also called the right vector, and the fourth one means the * * * yoke operator of p with a cross.