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Calculating an Infinite Box Extending Without Schrodinger

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Consider an infinte box extending from x=-a/2 to x=a/2. Can you, without actually solving the Schrodinger equation but by looking at the shape of the wave function, immediately give a general formula for the energy eigenvalues for an infinite box that extends for x=-a/2 to x=0? (Hint: Where do the eigenfunctions have nodes?)

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The solution calculates an infinite box extending without Schrodinger.

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The wave function must have nodes at the boundary of the box; and this implies that
only a half-integer number of ...

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