# 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 ψ

_{i}and ψ

_{j}corresponding to the energy values E

_{i}and E

_{j}respectively, the following conditions must be fulfilled-

∫Ψ

_{i}Ψ

_{j}d𝜏 = 0 -----Equation-1

This condition is called conditions of orthogonality of the wave functions. The two functions Ψ

_{i}and Ψ

_{j}are said to be orthogonal to each other.

When two wave functions Ψ

_{j}and Ψ

_{k}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 Ψ

_{j}and Ψ

_{k}will not necessarily be orthogonal.

The normalization and orthogonality conditions may be combined as-

∫Ψ

_{i}Ψ

_{j}d𝜏 = 1 if i = j

∫Ψ

_{i}Ψ

_{j}d𝜏 = 0 if i ≠ j

The wave function satisfy the above equation are said to be form orthonormal set of wave function.

**Share**