How did it happen!!!!!!

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How did it happen!!!!!!

Post by Sreejith A Nair on Thu Aug 25, 2016 10:53 pm

Can someone please tell me how
Y (x,t) became y (x)f (t).{I am using y for psy}

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Re: How did it happen!!!!!!

Post by The Confused Guy (O.o)? on Fri Aug 26, 2016 7:59 am

y(x,t) is a function of x and t so we can write it as a combination two funtion of each variable x and t
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Re: How did it happen!!!!!!

Post by Sreejith A Nair on Fri Aug 26, 2016 1:39 pm

But it need not always be a product of the two.

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Re: How did it happen!!!!!!

Post by Dinesh PR on Fri Aug 26, 2016 4:35 pm

Yes, you're right. But it's only a particular solution. If you add all possible solutions in this form, it's again mathematically a solution! And that's really the most general solution that incorporates all possible energies the electron can have!

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Re: How did it happen!!!!!!

Post by schrodinger on Fri Aug 26, 2016 4:40 pm

As electrons are considered standing waves , we can do the above.

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Re: How did it happen!!!!!!

Post by Confusions allowed on Sat Aug 27, 2016 12:00 pm

These pics are from Introduction to Quantum Mechanics, D. J. Griffiths, 2nd Ed. The first two explanations are physical, and the first was already discussed in the class. I'm not clear regarding the 3rd explanation, but 2nd seems promising. Also, the expectation value is a fancy term for average of a certain quantity in QM. The parts are as follows:
Part 1:

Part 2:


Part 3:


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Re: How did it happen!!!!!!

Post by Confusions allowed on Sat Aug 27, 2016 12:14 pm

One thing that I missed, to explain what is Normalization, which is mentioned in the text. Well, we do know that :
The infinite integral ∫|Ψ(x, t)|^2 dx has to be 1, as the electron is somewhere. But, the found solution may not give you that. Therefore, we devise a new Ψ' = AΨ, where A is a complex constant. We do know that Ψ appears on both the sides of the wave function, so one gets the same Physics as before. This can be used to get the total probability of finding the electron to be 1, which is called as Normalization.
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Re: How did it happen!!!!!!

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