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Re: plot dirac delta function? [message #49520 is a reply to message #49406]

Sat, 29 July 2006 22:27

swingnut
Messages: 30
Registered: September 2005

Member

kuyper@wizard.net wrote:
> swingnut@gmail.com wrote:
>> FYI, while the definition can be approached a number of equivalent
>> ways, the value of the Dirac IS "well-defined" at delta(x).
>> Technically, it's "well-defined" at the value such that its argument is
>> zero (which here is x=0).
>>
>> The value is indeed infinity. At least, that's how it's used in
>> physics.
>
> No, it is not. I'm very well versed in the use of the dirac delta
> function in physics, and the value of delta(0) is never used in any
> meaningful sense. Any equation which attempts to make use of the value
> at zero is meaningless. The dirac delta function only becomes
> meaningful after you've integrated over it.

FYI: the physical meaning of delta is used ALL the damn time when
you're talking about the spatial distribution of point particles (think
electrons and other extensionless subatomic particles here). If the
particle has no extension, as is generally believed to be true for,
e.g. electrons due to quantum considerations (classical radius of the
electron and arguments like that), then the only way to describe a mass
distribution is by summing up a bunch of things that are zero except
for at a single point in "configuration space" with no physical
extension. Following the logic, in any phase space, when the object's
parameters are point values in that space, you get the same behavior
for those parameters: a Dirac for the object's state. To say that
delta(x-a) just means that the particle is at x=a in that phase space;
x=0 refers to the origin of the phase space. These things are used all
the time or underly other calculations that are used all the time. If
you are using statistical mechanics at all, you should be seeing this
regularly.

Another physical application is as the Green's function corresponding
to Guass's law for a point charge, the mathematics of which gets
quickly generalized for minimum variance packet in quantum mech. The
fun just never stops.

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[Message index]

		plot dirac delta function? By: Nic on Wed, 19 July 2006 03:30
		Re: plot dirac delta function? By: James Kuyper on Sun, 23 July 2006 19:07
		Re: plot dirac delta function? By: swingnut on Sat, 29 July 2006 22:27
		Re: plot dirac delta function? By: swingnut on Sat, 29 July 2006 22:17
		Re: plot dirac delta function? By: James Kuyper on Sun, 30 July 2006 07:32
		Re: plot dirac delta function? By: Carsten Lechte on Fri, 11 August 2006 14:18
		Re: plot dirac delta function? By: James Kuyper on Sun, 30 July 2006 07:18
		Re: plot dirac delta function? By: James Kuyper on Fri, 11 August 2006 15:35
		Re: plot dirac delta function? By: priorbee on Fri, 25 November 2016 02:13

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