Delta Dirac: $\phi=-\pi+\epsilon$

[alejandrito29]

if \phi is a angular coordinate , between (-\pi,\pi)

¿how much is \delta(\phi-\pi) with \phi=-\pi+\epsilon?

 

[SpectraCat]

The Dirac delta function yield zero unless it's argument is zero, in which case it yields 1 (this is an oversimplification, but it should do for the present discussion). In your case, the argument of the delta function is -2*\pi + \epsilon, so it should be zero. Did you mean to type, \phi=\pi + \epsilon? In that case, the argument of the delta function would be just \epsilon, and then you need to get a bit more specific about how you are defining the delta function. Have you looked at this thread? https://www.physicsforums.com/showthread.php?t=73447

 

[alejandrito29]

The Dirac delta function yield zero unless it's argument is zero, in which case it yields 1 (this is an oversimplification, but it should do for the present discussion). In your case, the argument of the delta function is -2*\pi + \epsilon, so it should be zero. Did you mean to type, \phi=\pi + \epsilon? In that case, the argument of the delta function would be just \epsilon, and then you need to get a bit more specific about how you are defining the delta function. Have you looked at this thread? https://www.physicsforums.com/showthread.php?t=73447

then the dirac delta evaluated in (-2pi+epsilon) is 0 or infinite?

 

[alejandrito29]

specifically, i need to find T, in the follows equation:

\delta(\phi-\pi)+k=T\delta(\phi-\pi)
where \phi is between (-\pi,\pi)

 

[haushofer]

With that specific range the delta distribution is zero; phi can't become equal to pi. So you get the equation 0 + k = T*0.

 

[alejandrito29]

With that specific range the delta distribution is zero; phi can't become equal to pi. So you get the equation 0 + k = T*0.

but, if i do:

\int^{\pi-\epsilon}_{-\pi+\epsilon}\delta(\phi-\pi)d\phi+\int^{\pi-\epsilon}_{-\pi+\epsilon} k=T\int^{\pi-\epsilon}_{-\pi+\epsilon}\delta(\phi-\pi)

is correct??

pd: \phi can be equal to \pi...\phi is between (-\pi,\pi)

 

[Matterwave]

You want to integrate from pi-epsilon to pi+epsilon. That will include the relevant range of the dirac delta.