Readings: Chapters $10,12(21,23)$ in E&R

Problem $1-$ Wavefunction Symmetry

Which of the following functions are $($i$)$ symmetric $($ii$)$ antisymmetric $($iii$)$ neither

$($a$)e^{-b(r_1-r_2)}$

$($b$)[f(1)g(2)-g(1)f(2)][(1)(2)-(2)(1)]$

$($c$)r_{12}^2{e}^{-b(r_1+r_2)}$

$($d$)[f(1)g(2)+g(1)f(2)][(1)(2)-(1)(2)+(1)(2)]$

$($e$)f(1)g(2)(1)(2)$

$($f$)f(1)f(2)[(1)(2)-(1)(2)]$

$($g$)f(1)f(2)f(3)(1)(2)(3)$

in the interchange of electron space$-$spin coordinates, where $r_1=|x_1|,r_2=|x_2|,$ and $r_{12}=|x_1-x_2|.$