Chapter 12, Problem 12.17E

If ${\varphi }_1$ and ${\varphi }_2$ are the individual wavefunctions for electron $1$ and electron $2$, identify each overall wavefunction $\Psi$ as symmetric or antisymmetric with respect to exchange of the two electrons. (i.e., ${\varphi }_1$ becomes ${\varphi }_2$ and vice versa).

(a) $\Psi ={\varphi }_1+{\varphi }_2$

(b) $\Psi ={\varphi }_1-{\varphi }_2$

(c) $\Psi ={\varphi }_1{}^2+{\varphi }_2{}^2$

(d) $\Psi =\sin {\varphi }_1+\sin {\varphi }_2$

(d) $\Psi =\cos {\varphi }_1-\cos {\varphi }_2$