Question

is cos(ax)cos(bx)cos(cz) an eigen function in Laplacian operator?

Answer 1

Show that (cos ax)(cos bx)(cos cz) is an eigenfunction of the Laplacian operator bigtriangledown ^2 = partial^2 /partial x^2 + partial^2 /partial y^2 + partial^2 /partial z^2 . An eigenfunction psi _a =a psi _a , where a is a scalar called the 'eigenvalue'.