Let be a non-zero vector. To normalize is to find the unique unit vector with the same direction as . This is done by multiplying by the reciprocal of its length; the corresponding unit vector is given by .
The concept of a unit vector and normalization makes sense in any vector space equipped with a real or complex norm. Thus, in quantum mechanics one represents states as unit vectors belonging to a (possibly) infinite-dimensional Hilbert space. To obtain an expression for such states one normalizes the results of a calculation.
Consider and the vector . The norm (length) is . Normalizing, we obtain the unit vector pointing in the same direction, namely .
|Date of creation||2013-03-22 11:58:50|
|Last modified on||2013-03-22 11:58:50|
|Last modified by||rmilson (146)|