## Wave Function

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

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

Keon Amirazodi 2H
Posts: 44
Joined: Wed Sep 30, 2020 9:59 pm

### Wave Function

Can anyone explain what exactly the wave function represents and how that relates to orbitals of electrons? Also, what does electron density distribution mean?

Sara_Lim_3K
Posts: 40
Joined: Wed Sep 30, 2020 9:55 pm

### Re: Wave Function

I was wondering the same thing, commenting so I can find this post later

Hayden Lee 1C
Posts: 40
Joined: Wed Sep 30, 2020 9:57 pm

### Re: Wave Function

Hi!

Simply put, the wave function is a mathematical expression that describes the state of an electron. It is a function that defines the probability of a particle's quantum state. This is done by incorporating the following factors: the energy of an electron, the angular momentum, orbital orientation, and spin. Electron density distribution is the probability of an electron being present in the space around a given point. For example, p- and d- orbitals have nodal planes, giving them asymmetric electron distributions. Hope this helps!

SophiaJenny1J
Posts: 56
Joined: Wed Sep 30, 2020 9:56 pm
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### Re: Wave Function

Hi! So basically wave functions are orbitals. The wave function of an electron squared (Ψ^2) is the probability plot of finding the electron. So, if you see this graph or plot here's a basic explanation of how to read it. If you picture a regular wave, there is a node and a peak as well as the curved line connecting the two. The node has a low probability of having an electron and the peak has a high probability of having an electron, and this general trend continues throughout. The higher on the wave you are, the more probability of an electron. In the s orbital, there is an equal probability of an electron begin anywhere in the s orbital because it's a sphere and in this sense equally distant from the nucleus. In the p orbital, this is where it gets a bit different. Picture the p orbital as kind of like an infinity sign on a graph (if you're looking at it 2-dimensionally). The center point would have a very low probability of finding an electron because it's so close to the nucleus. As you get closer to the nucleus, the probability goes down. The places to find high probability of finding an electron is kind of hard to describe so I just attached a picture below (look at the brackets within the infinity sign)! Hope this helps!!!
Attachments

AHUNT_1A
Posts: 48
Joined: Wed Sep 30, 2020 9:41 pm

### Re: Wave Function

Sara_Lim_3K wrote:I was wondering the same thing, commenting so I can find this post later

same!

Xavier Herrera 3I
Posts: 41
Joined: Wed Sep 30, 2020 9:37 pm

### Re: Wave Function

So, looking at the slides from the lecture, the wave function represents the height of the electron's wave at x,y,z. Each way of solving the wave function gives you a different orbital, so solving the wave function one way will give you the s orbital, and solving another way will give you the p orbital. The square of the wave function represents the probability of finding an electron. This would give you the actual probability regions of the orbital, with the nodes that represent a 0% probability of finding an e-