Conditions of Orthogonality of Wave Functions

Conditions of Orthogonality of Wave Functions

Conditions of Orthogonality of Wave Functions

Conditions of Orthogonality of Wave Functions

There may be number of acceptable solutions to Schrodinger equation Hψ = Eψ for a particular system. Each wave function ψ has a corresponding energy value E.
For any two wave functions ψi and ψj corresponding to the energy values Ei and Ej respectively, the following conditions must be fulfilled-
∫ΨiΨjd𝜏 = 0      -----Equation-1
This condition is called conditions of orthogonality of the wave functions. The two functions Ψi and Ψj are said to be orthogonal to each other.
When two wave functions Ψj and Ψk corresponds to the same energy E. The system in such an energy state is said to be degenerate state. In such a situation, the degenerate wave functions Ψj and Ψk will not necessarily be orthogonal.
The normalization and orthogonality conditions may be combined as-
∫ΨiΨjd𝜏 = 1      if i = j
∫ΨiΨjd𝜏 = 0      if i ≠ j
The wave function satisfy the above equation are said to be form orthonormal set of wave function.

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