Notice that in deriving the wave equation we replaced the number or by a differential acting on the wave function. The energy (or rather the Hamiltonian) was replaced by an ”operator”, which when multiplied with the wave function gives a combination of derivatives of the wave function and function multiplying the wave function, symbolically written as
(3.16) |
This appearance of operators (often denoted by hats) where we were used to see numbers is one of the key features of quantum mechanics.