Separation of variable

Separation of variable

Two dimensional Laplace’s equation in Cartesian Co-ordinates.

 Let us consider a wave function ψ . Where ψ = ψ ( x , y )

Then the Laplace’s equation can be written as

s ² ψ = 0

Or in other words we can write as

( ∂ ² ψ / ∂ x ² ) + ( ∂ ² ψ / ∂ y ² ) = 0  _ _ _ _ _ _ _  ( 1 )