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Topic: Variational Method  (Read 1768 times)

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Offline BetaAmyloid

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Variational Method
« on: October 10, 2012, 07:18:50 PM »
Hello everyone,

So I have a normalized wavefunction phi(x). I am told what [Integral (phi)*H(phi)] is. I am supposed to approximate the ground state energy of such function. I know [Integral (phi)*H(phi)]/[Integral (phi)*(phi)] = Energy. If phi(x) is normalized then the denominator should be 1. I have taken the derivative of the numerator (which is the only thing left now that the denominator is one) and received two values (a negative value and a positive value). I plugged these values from the derivative of the energy back into the original [Integral (phi)*H(phi)] function to receive what I thought should be the energy approximation. I basically get 4.94 when the REAL result of the ACTUAL wavefunction is 0.125. Does my process seem to be correct?

I am not listing the actual problem here because it is a homework problem that others have and I want them to work it out fully rather than searching and finding this site on google.

Thank you for your input.
Discovery consists of seeing what everybody has seen and thinking what nobody has thought - Albert Szent-Györgyi

Offline BetaAmyloid

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Re: Variational Method
« Reply #1 on: October 10, 2012, 09:12:47 PM »
Nevermind! I forgot to square some of the terms...

Got it now though, thanks.
Discovery consists of seeing what everybody has seen and thinking what nobody has thought - Albert Szent-Györgyi

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