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Consider the wave function (x, y) = cos(a x) cos(b y), where a = 5, b = 2.
(a) Show that (x, y) is an eigenfunction of the 2D Laplacian operator, V² =
find its eigenvalue, using the values of a and b.
d²
(b) Evaluate the operation of Â = (x² + on y(x) = sin(a x) and determine if
2² 2²
+
0x2 дуг'
and
(x) is
dx²
an eigenfunction of this operator. If it is, provide an expression for its eigenvalue as a
function of a. If it is not, why is it not an eigenfunction?

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