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# Eigen Function The various values of ψ which have been derived from the wave equation corresponding to definite values of energy are called eigen functions. ## Operator - A f(x) = a f(x) ## Normalization A wave function is said to be normalized if integration of |ψ|² (οπ ψ ψ²) with respect to...

# Eigen Function The various values of ψ which have been derived from the wave equation corresponding to definite values of energy are called eigen functions. ## Operator - A f(x) = a f(x) ## Normalization A wave function is said to be normalized if integration of |ψ|² (οπ ψ ψ²) with respect to element vector dτ = dx dy dz over the whole of the space -x to +∞ is unique writ. +∞ ∫ ψ²dτ = 1 -∞ ## Orthogonalization If there are two wave functions ψ₁ and ψ₂ complex conjugate ψ₁*, ψ₂* respectively then the two will be orthogonal to each other and satisfy if the following condition- +∞ ∫ ψ₂ψ₁* dτ = 0 -∞ ## Significance of ψ and ψ² The wave function ψ does not have any physical significance but has only mathematical significance only. However, ψ² at any point tells about the probability of finding an electron. ψ² α electron density