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orthocresol
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Why istis the helium wavefunction a linear combination?

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Wildcat
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the general solution for the wave function of Helium is a linear combination of the two possible states: [![][1]][1] [1]: https://i.sstatic.net/1Jdyo.png

$$ \text{state 1:} \quad \psi_a(\vec{r}_{1}) \, \psi_b(\vec{r}_{2}) \\ \text{state 2:} \quad \psi_a(\vec{r}_{2}) \, \psi_b(\vec{r}_{1}) $$

(where r1/r2$\vec{r}_{1}/\vec{r}_{2}$ denotes electron 1/2.)

But aren't the products of these wavefunction the same? Why then make a linear combination; it would be just like same function +/- same function?

enter image description here$$ \psi_a(\vec{r}_{1}) \, \psi_b(\vec{r}_{2}) = \psi_a(\vec{r}_{2}) \, \psi_b(\vec{r}_{1}) \, ? $$

the general solution for the wave function of Helium is a linear combination of the two possible states: [![][1]][1] [1]: https://i.sstatic.net/1Jdyo.png

(where r1/r2 denotes electron 1/2.)

But aren't the products of these wavefunction the same? Why then make a linear combination; it would be just like same function +/- same function?

enter image description here

the general solution for the wave function of Helium is a linear combination of the two possible states:

$$ \text{state 1:} \quad \psi_a(\vec{r}_{1}) \, \psi_b(\vec{r}_{2}) \\ \text{state 2:} \quad \psi_a(\vec{r}_{2}) \, \psi_b(\vec{r}_{1}) $$

(where $\vec{r}_{1}/\vec{r}_{2}$ denotes electron 1/2.)

But aren't the products of these wavefunction the same? Why then make a linear combination; it would be just like same function +/- same function?

$$ \psi_a(\vec{r}_{1}) \, \psi_b(\vec{r}_{2}) = \psi_a(\vec{r}_{2}) \, \psi_b(\vec{r}_{1}) \, ? $$

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hanna
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Why ist the helium wavefunction a linear combination?

the general solution for the wave function of Helium is a linear combination of the two possible states: [![][1]][1] [1]: https://i.sstatic.net/1Jdyo.png

(where r1/r2 denotes electron 1/2.)

But aren't the products of these wavefunction the same? Why then make a linear combination; it would be just like same function +/- same function?

enter image description here