Casimir effect with Gaussian regulator

Silviu
Messages
612
Reaction score
11

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.
 
Physics news on Phys.org
Check it in Voja's problem book under regularization.
 
I didn't find it there...
 

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Thread 'Help to convert units of a simple formula'

The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
View full post »

Similar threads

Please tell me where I am going wrong in this integral
Replies
2
Views
111
I The dispersion interaction and Casimir effect
Replies
10
Views
3K
Solving a Gaussian integral using a power series?
Replies
9
Views
3K
Showing that this identity involving the Gamma function is true
Replies
1
Views
1K
Amplitude of Feynman diagram in ##\phi^4## interactions
Replies
2
Views
3K
Fourier Transform of a Gaussian Pulse
Replies
2
Views
4K
Finding the wave function for a Gaussian wave packet
Replies
6
Views
6K
(Quantum Mechanics) Gaussian Distributions, Expected Values, and Sketches
Replies
2
Views
6K
Capacitance of a parallel-plate Capacitor with non uniform dielectric
Replies
17
Views
4K
Boltzmann Partition Function of H_2
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top