## Electron Density

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

Parth Mungra
Posts: 72
Joined: Fri Sep 28, 2018 12:28 am

### Electron Density

In the beginning of Wednesday's lecture, we went over that we have a math model that represents a wave function. I was confused on how we went from the wave function to the probability of finding the electron just by squaring the original math model. I'm confused because squaring a function changes the shape, but doesn't change the representation of the the function. In simpler terms, how did we get to the probability of the finding an electron (electron density)?

Chem_Mod
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### Re: Electron Density

To find the probability of electron density, you take the wave function (Ψ aka height of the wave) in the Schrodinger equation, and square Ψ. Calculate Ψ2, which represents the probability of finding an electron in a specific location in an atom (ex. for a p-orbital, at x=0, since there's a node there, the Ψ2=0, since height at x=0 is 0, Ψ=0).