Casimir effect with Gaussian regulator

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Homework Help Overview

The discussion revolves around calculating the Casimir force in one dimension using a Gaussian regulator. The original poster attempts to evaluate a specific sum involving an exponential function, seeking assistance in progressing towards a solution.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the evaluation of a sum of the form $$\sum_n n e^{-\epsilon^2n^2}$$ and the original poster considers transforming it into a Gaussian integral. There are suggestions to check specific resources and to use Abel's summation formula, indicating a search for alternative methods.

Discussion Status

The discussion is ongoing, with participants offering references and methods to explore further. There is no explicit consensus on the approach, and multiple interpretations of the problem are being considered.

Contextual Notes

The original poster expresses difficulty in finding useful information online and mentions a specific resource that did not provide the needed clarity. This indicates potential constraints in available references or understanding of the topic.

Silviu
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Homework Statement


Calculate the Casimir force in 1D using a Gaussian regulator.

Homework Equations

The Attempt at a Solution


I reached a point where I need to evaluate a sum of the form $$\sum_n n e^{-\epsilon^2n^2}$$ Can someone help me? I didn't really find anything useful online. I thought of turning this into a gaussian integral, and I would get something of the form ##\frac{1}{\epsilon}\frac{\sqrt{\pi}}{2}##, but I don't get the answer I need using this.
 
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Check it in Voja's problem book under regularization.
 
I didn't find it there...
 

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