Notice that in deriving the wave equation we replaced the number p or
k 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
(x, t) = - (x, t) + V(x)(x, t).
(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.