91影视

The fundamental equation for characterizing quantum mechanical phenomena is the Schrodinger equation. It is a partial differential equation that illustrates how a physical system's wave function changes over time. The electron is a wave in the three-dimensional space surrounding the nucleus.

${\mathrm{蠄}}_{卤}=\mathrm{A}\left[\mathrm{蠄}\left({\mathrm{r}}_1,{\mathrm{r}}_2,{\mathrm{r}}_3,..{\mathrm{r}}_{\mathrm{z}}\right)卤\mathrm{蠄}\left({\mathrm{r}}_2,{\mathrm{r}}_1,{\mathrm{r}}_3,..,{\mathrm{r}}_{\mathrm{z}}\right)+\mathrm{蠄}\left({\mathrm{r}}_2,{\mathrm{r}}_3,{\mathrm{r}}_1,..,{\mathrm{r}}_{\mathrm{z}}\right)+\mathrm{etc}.\right],$

Where etc. runs over all permutations of the arguments,$\left({\mathrm{r}}_1,{\mathrm{r}}_2,..,{\mathrm{r}}_{\mathrm{z}}\right)$ with a + sign for all even permutations (even number of transpositions $r_i鈫�r_j$starting from $\left({\mathrm{r}}_1,{\mathrm{r}}_2,..,{\mathrm{r}}_{\mathrm{z}}\right)$and 卤 for all odd permutations (+ for bosons, 鈥� for fermions).

At the end of the process, normalize the result to determine A. (Typically $A=1/\sqrt{Z!}$, but this may not be right if the starting function is already symmetric under some interchanges.)

If 蠄 is symmetric in the first two arguments (or any other pair), the anti symmetric combination is zero.

For example, if Z = 3,

${\mathrm{蠄}}_{-}=蠄\left[\mathrm{蠄}\left({\mathrm{r}}_1,{\mathrm{r}}_2,{\mathrm{r}}_3\right)-\mathrm{蠄}\left({\mathrm{r}}_2,{\mathrm{r}}_1,{\mathrm{r}}_3\right)+\mathrm{蠄}\left({\mathrm{r}}_2,{\mathrm{r}}_3,{\mathrm{r}}_1\right)-\left({\mathrm{r}}_3,{\mathrm{r}}_1,{\mathrm{r}}_2\right)+\mathrm{蠄}\left({\mathrm{r}}_3,{\mathrm{r}}_1,{\mathrm{r}}_2\right)-\mathrm{蠄}\left({\mathrm{r}}_1,{\mathrm{r}}_3,{\mathrm{r}}_2\right)\right]=0$

(They cancel in pairs).