Conditions of Normalization of Wave Functions
Conditions of Normalization of Wave Functions
Normalizing the wave function means probability of finding an electron in limited area (i.e. somewhere in space) is one. So, the normalization is possible when there are some boundary conditions placed on the particle.If Ψ2dx or ΨΨ*dx represents the probability of finding a particle at any point 'x', then the integration over the entire range of possible locations, i.e. the total probability must be unity because the particle has to be somewher within that range. i.e.
∫Ψ2dx = 1 -----Equation-1
or, ∫ΨΨ*dx = 1 -----Equation-1
In three dimensions, ∫Ψ2d𝜏 = 1
where, d𝜏 = dx. dy. dz.
A wave function which satisfies the equation-1 is called a normalized wave function and this condition is called normalization condition.
If after the solving the Schrodinger wave equation, the wave function does not satisfy the equation-1, it must be multiplied by a constant factor called normalization factor 'N'.
If a function ∫Φ2dx = c and c is not equal to 1
then the normalization factor will be 1/√c and the normalized wave function will be-
(1/√c)Φ
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