nLab
unit vector

Contents

Definition

Let VV be a normed vector space. A unit vector in VV is a vector with norm of 1. Given a non-zero vector vVv \in V, we can normalize it to a unit vector v|v|\frac{v}{|v|} in the same direction.

In quantum mechanics

Classically, the space of states of a quantum-mechanical system is given by a Hilbert space HH. Often, it is desirable to consider only states of unit norm. One can view this as requiring that probabilities sum up to 1.

Last revised on September 6, 2016 at 07:29:36. See the history of this page for a list of all contributions to it.