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aayyappan1-Visitor
1-Visitor
August 12, 2014
Question

Variational method

Hello to all,

I hope I can get some help here. I created a worksheet in mathcad for variational method.

Actually I am know only the basic about mathcad. In my worksheet , the minimization couldnot be able to do,

it take too much of time to do the minimization. Finally I am not able to get the answer.

So please see my attachement and help me to get the answer.

Thank you


8 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
August 12, 2014

Have you ever tried to evaluate your function E(a) for any single position of a?

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aayyappan1-VisitorAuthor
1-Visitor
August 13, 2014

Yes, I have tried that. But the forth term of E, which shows some error.

so coudnot get the answer. is that a problem for minimization?. If it means What shall I do? see the attachment i have tried for a=2.

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AlanStevens19-Tanzanite
19-Tanzanite
August 12, 2014

I've simplified your integrals as much as possible; replaced them by discrete summations (with a really coarse resolution!) ; and they still take a while to evaluate! See attached. Incidentally the kernels of your inner integrals in E are independent of the variable over which you are integrating, so these inner integrals can just be replaced by 2pi.

See attached.

Alan

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aayyappan1-VisitorAuthor
1-Visitor
August 13, 2014

Alan Thank you for time consideration to solve my problem. You did a great work for me.

you replaced -Zinf by 2 and Pinf by 10. But in my problem it should be infinity only.

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AlanStevens19-Tanzanite
19-Tanzanite
August 13, 2014

Anitha Ayyappan wrote:

Alan Thank you for time consideration to solve my problem. You did a great work for me.

you replaced -Zinf by 2 and Pinf by 10. But in my problem it should be infinity only.

Yes, as it stands you will probably have to wait for an infinite time for the program to work if you use infinite (or very large) limits. The important question is: do the results change as these limits get bigger? Once the results stop changing (if they do) then you can safely use finite limits.

I did a little more work and simplified a few more things in your worksheet - see attached. Now you can use slightly larger limits and increase the resolution of the discrete sum representation of E (again, you need to keep increasing the resolution until the results don't change).

Calculation speed has increased, but is still fairly low!

Alan

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-MFra-21-Topaz II
21-Topaz II
August 20, 2016

Hi Anitha Ayyappan,

perhaps modifying your trial wave function (without discontinuities) you can obtain some results as in the following immage:

aayyappan.jpg

PS: you have to modify the normalization integral.

Bye

FM

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