Wave function ↩

Metadata

shorthands: {}
aliases: [wave function]
created: 2021-12-11 00:56:36
modified: 2022-01-11 17:15:30

In quantum mechanics, the state of a system or a particle is described by its wave function. The wave function is usually notated by

and it is a vector in Hilbert space

. The time-development of the system is described by the Schrödinger equation.

Position-space wave function

Let's consider the case of a single particle without spin. In this case, the wave function is a square-integrable function, in the space, that is a Hilbert space. denotes the dimension of the system. The wave function:

Where is position and is time.

Quantum states as vectors

We usually use the Bra-ket notation for denoting quantum mechanical states. These are abstract vector in the Hilbert space, and element of its dual space, so that

Is their inner product.