Editing Wave function (section)

====Normalization condition====
The probability that its position {{math|''x''}} will be in the interval {{math|''a'' ≤ ''x'' ≤ ''b''}} is the integral of the density over this interval:
<math display="block">P_{a\le x\le b} (t) = \int_a^b \,|\Psi(x,t)|^2 dx </math>
where {{mvar|t}} is the time at which the particle was measured. This leads to the '''normalization condition''':
<math display="block">\int_{-\infty}^\infty \, |\Psi(x,t)|^2dx  = 1\,,</math>
because if the particle is measured, there is 100% probability that it will be ''somewhere''.

For a given system, the set of all possible normalizable wave functions (at any given time) forms an abstract mathematical [[vector space]], meaning that it is possible to add together different wave functions, and multiply wave functions by complex numbers. Technically, wave functions form a [[Mathematical formulation of quantum mechanics#Description of the state of a system|ray]] in a [[projective Hilbert space]] rather than an ordinary vector space.