Exchange Forces

#Physics

$\displaystyle {\left\langle{(\Delta x)^{2}}\right\rangle}{\pm }={\left\langle{(\Delta x)^{2}}\right\rangle}{d}\mp 2\lvert {\left\langle{x}\right\rangle}_{ab}\rvert^{2}$

• The variance in position of a two state system for either bosons ($\displaystyle +$) or fermions ($\displaystyle -$) is given by the variance in position for the distinguishable particle case $\displaystyle \mp$ a correction factor
• Net effect is attraction between bosons and repulsion between fermions

$\displaystyle {\left\langle{x}\right\rangle}{ab}\equiv \int x\psi{a}(x)^{*}\psi_{b}(x) , \mathrm{d}x$