**Probability density** __One electron in one spatial dimension:__ ψ(x) : the spatial wavefunction describing with the electron

x : the only degree of freedom (e.g. movement along the x-axis) that the electron has

The probability of finding the electron in a particular point x is:

P(x)dx = |ψ(x)|

^{2}dx

The probability to find the electron in an interval [a,b] is:

P

_{ab} =

_{a}∫^{b}|ψ(x)|

^{2}dx

__One electron in three spatial dimensions:__ ψ(x,y,z) : the spatial wavefunction describing with the electron

The probability of finding the electron at a particular point defined by the vector r is:

P(r)dr = |ψ(r)|

^{2}dr

The probability to find the electron in a volume V is:

P

_{V} =

∫_{V}|ψ|

^{2}dV

__Two distinguishable electrons in three spatial dimensions:__ ψ(x

_{1},y

_{2},z

_{3},x

_{2},y

_{2},y

_{3}) : the spatial wavefunction describing with the electrons

(x

_{1},y

_{2},z

_{3}) : position of electron 1

(x

_{2},y

_{2},y

_{3}) : position of electron 2

The probability of finding the electron 1 at a particular point defined by the position vector r

_{1} and at the same time finding electron 2 at a particular position vector r

_{2} is:

P(r

_{1},r

_{2})dr

_{1}dr

_{2} = |ψ(r

_{1},r

_{2})|

^{2}dr

_{1}dr

_{2} The probability to find electron 1 in a volume R and to find sumultaneously electron 2 in a volume S is:

P

_{RS} =

∫_{R}∫_{S}|ψ|

^{2}dV

_{1}dV

_{2} __See also:__ Wavefunction

http://en.wikipedia.org/wiki/Wavefunction