The general form for symmetric and antisymmetric wave functions is ψn(x1) ψn(x2) ± ψn(x1) ψn(x2), but it is not normalized, (a) In applying quantum mechanics, we usually deal with quantum states that are "orthonormal." That is, if we integrate over all space the square of any individual-particle function, such as ψn*(x) ψn(x) or ψn we get but for the product of different individual-particle functions, such as ψn*(x) ψn(x) we get 0. This happens to be true for all the systems in which we have obtained or tabulated sets of wave functions (e.g., the particle in a box, the harmonic oscillator, and the hydrogen atom). Assuming that this holds, what multiplicative constant would normalize the symmetric and antisymmetric functions? (b) What value A gives the vector V = A(x ± y) unit length? (c) Discuss the relationship between your answers in (a) and (b).
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