## Wave function

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

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

Melody Haratian 3K
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### Wave function

Hi everyone!
I‘m reviewing schrodinger’s equation but I’m having trouble understanding some key parts of the equation What is a wave function and how does it relate to the electron? Also, what does Dr. Lavelle mean by a change in the wave function?

Farah Abumeri 1B
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### Re: Wave function

Hi Melody!
A wave function (trident symbol) is a math model that describes an electron's position, momentum, and wavelike properties in an atom. I think Dr. Lavelle is referring to how a wave function can be positive or negative or 0 according the phase of the wave when he says change in wave function. I think another important thing to know about Schrodinger's equation is that the Hamiltonian (which means double or second derivative) of the wave function equals the energy of the wave function. Also, we can compare this energy to verify it with the atomic spectra experiment. I hope this answers your question.

TrishaP_3E
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Joined: Wed Sep 30, 2020 9:58 pm

### Re: Wave function

I think also conceptually, a wave function is a mathematical representation of an electron orbital, and the probability density of an electron within it.

FionaHunter21
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Joined: Wed Sep 30, 2020 9:37 pm

### Re: Wave function

Right now, can we consider the wave function to just be simplified to the version where we treat it like a sine function?

Binyu You
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Joined: Wed Sep 30, 2020 9:37 pm

### Re: Wave function

I think the wave function is just representing the electron orbital, and the symbol of psi represents the wave while the square of psi (the symbol)represents the probability of finding an electron.

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

### Re: Wave function

The psi symbol is the wave function, which represents the probability region and momentum of an electron. I understand that the hamiltonian is the left part of Schrodinger's Equation, but I don't understand what people mean when they say it is the second derivative.

Isabelle Hales 3L
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### Re: Wave function

Hi. I am still a bit confused about this. Is it correct to say that the Hamiltonian value represents the probability of finding the electron while the energy wave function represents the orbital itself? It would be great if someone could explain what exactly the equation is representing with the two wave functions.

reyvalui_2g
Posts: 35
Joined: Wed Sep 30, 2020 9:52 pm

### Re: Wave function

FionaHunter21 wrote:Right now, can we consider the wave function to just be simplified to the version where we treat it like a sine function?

Yes, I think it would be safe to assume that for now since the way we are trying to understand the wave function is by using the "particle in a box" analogy.

FionaHunter21
Posts: 34
Joined: Wed Sep 30, 2020 9:37 pm

### Re: Wave function

Isabelle Hales 3L wrote:Hi. I am still a bit confused about this. Is it correct to say that the Hamiltonian value represents the probability of finding the electron while the energy wave function represents the orbital itself? It would be great if someone could explain what exactly the equation is representing with the two wave functions.

I believe that the solutions to the wave function are the orbitals, and the wave function squared represents the probability of finding an electron in a given space, but I don't know how to explain why. I'm not sure what the Hamiltonian equation represents exactly.