Use the method of separation of variables to construct the energy eigenfunctions for the particle trapped in a 2D box. In other words, solve the equation: -h? ( a?»(x, y) + a²ª„(x, y) dy? En Pn (x, y), 2m dx² such that the solution is zero at the boundaries of a box of 'width' L, and 'height' Ly. You will see that the 'allowed' energies En are quantized just like the case of the 1D box. It is most convenient to to place the box in the first quadrant with one vertex at the origin.

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