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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 function. ### Operator * A f(x) = a f(x) ### Normalization A wave function is said to be normalized if the integration of J$²- (Ψ * Ψ)$ with resp...

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