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Probability density (Read 3534 times)
Gerrit-Jan Linker
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Probability density
06.03.08 at 13:02:34
 
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)|2dx
 
The probability to find the electron in an interval [a,b] is:
Pab = ab|ψ(x)|2dx
 
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)|2dr
 
The probability to find the electron in a volume V is:
PV = V|ψ|2dV
 
Two distinguishable electrons in three spatial dimensions:
ψ(x1,y2,z3,x2,y2,y3) : the spatial wavefunction describing with the electrons
(x1,y2,z3) : position of electron 1
(x2,y2,y3) : position of electron 2
 
The probability of finding the electron 1 at a particular point defined by the position vector r1 and at the same time finding electron 2 at a particular position vector r2 is:
P(r1,r2)dr1dr2 = |ψ(r1,r2)|2dr1dr2
 
The probability to find electron 1 in a volume R and to find sumultaneously electron 2 in a volume S is:
PRS = RS|ψ|2dV1dV2
 
See also:
Wavefunction
http://en.wikipedia.org/wiki/Wavefunction
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« Last Edit: 06.03.08 at 13:23:23 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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