Editing Function of a real variable (section)

==Banach and Hilbert spaces and quantum mechanics==
Generalizing the previous section, the output of a function of a real variable can also lie in a [[Banach space]] or a [[Hilbert space]]. In these spaces, division and multiplication and limits are all defined, so notions such as derivative and integral still apply. This occurs especially often in quantum mechanics, where one takes the derivative of a [[bra–ket notation|ket]] or an [[operator (physics)|operator]]. This occurs, for instance, in the general time-dependent [[Schrödinger equation]]:

:<math>i \hbar \frac{\partial}{\partial t}\Psi = \hat H \Psi</math>

where one takes the derivative of a wave function, which can be an element of several different Hilbert spaces.