## Clarification Needed..

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

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

Ian_Lee_1E
Posts: 109
Joined: Wed Sep 30, 2020 9:31 pm

### Clarification Needed..

Can someone help me understand Shrodinger Equation?

Professor talked about how the wave function represents the height of a wave at point xyz and how wave function squared is the PROBABILITY of finding an e- which i have no clue why.

Also, why does deriving matter? what about a sin function derived to cosine derived back to sin that matters in this equation?

Lucy Wang 2J
Posts: 86
Joined: Wed Sep 30, 2020 10:09 pm
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### Re: Clarification Needed..

I asked my TA about this and I think he was just explaining how they got the equation but for this class we won't necessarily need to know how to derive it. I think the wave is to represent the probability that you will find an electron there. So at the peaks, it has the greatest probability and when it hits zero, there is very little to no probability there is an electron at that location. So essentially, Schrodinger's equation is just used to determine that an electron is located in an area.

Yashvi Reddy 1H
Posts: 93
Joined: Wed Sep 30, 2020 9:40 pm
Been upvoted: 1 time

### Re: Clarification Needed..

I agree with the post above! In addition, Schrodinger's Wavefunction Equation basically uses the concept that an e-, with wavelike properties and indeterminacy in momentum and position, can be described by a wave function. Wherever ψ^2 is large, the particle has a high probability density; wherever ψ^2 is small, the particle has only a low probability density. The textbook states the Born Interpretation, which if I'm not wrong, is what you seem to be referring to. It is as follows: "the probability of finding the particle in a region is proportional to the value of ψ^2 in that region. To be precise, ψ^2 is a probability density, the probability that the particle will be found in a small region divided by the volume of the region." I hope this helps!

Christine Ma 3L
Posts: 87
Joined: Wed Sep 30, 2020 9:35 pm

### Re: Clarification Needed..

For your deriving question, I think Dr. Lavelle brought up the sine and cosine derivatives to demonstrate how the hamiltonian in Schrodinger's equation works (the H in the equation).
Hψ contains a double derivative function (among other operations) inside, and the wave function ψ is returned in the answer (=Eψ) just like how the double derivative of a sine function returns sine.
Hope this helps!