What is meant by first momentum of energy spectrum (ES)

[Rajini]

Hello all,

I wanted to know
what is meant by first momentum of energy spectrum (ES),
second momentum of ES, and also third momentum of ES.
It will be nice with some references, books, etc.

thanks

 

[K^2]

For any function of single variable, f(x), you can find an n-th moment μ_n using this formula.

$$\mu_n = \int_{-\infty}^{\infty} x^n f(x) dx$$

 

[AJ Bentley]

For any function of single variable, f(x), you can find an n-th moment μ_n

Never seen that before.
What's the significance of it in relation to a spectrum?

 

[Dickfore]

It's called moment, not momentum. Momentum is a different physical quantity and moment is a statistical function. The energy spectrum is treated like some probability distribution function.

 

[Rajini]

Hi force and k2,
i got some idea from you reply.
Yes it should be moment and not momentum.

 

[K^2]

What's the significance of it in relation to a spectrum?

Provided that spectrum is normalized, that is μ₀=1, μ₁=<E>, μ₂=<E²>, and consequently, ΔE=sqrt(μ₂-μ₁²). I have no idea what the significance of the 3rd moment is.

 

[Dickfore]

I have no idea what the significance of the 3rd moment is.

http://en.wikipedia.org/wiki/Moment_(mathematics)#Skewness"

 

[K^2]

Yes, I'm aware of the name of the 3rd moment. I'm not sure what relevance it has specifically to the energy distribution spectrum. <E> and ΔE have very specific physical consequences. I'm not sure if the same can be said about <E³>.

 

[Dickfore]

So, what is the physical significance of the first and the second moment?

 

[Rajini]

Hi force,
from nis (nuclear inelastic scattering), from 2nd moment of the spectrum you get the mean force constant of the Mössbauer nucleus and from 3rd you get mean square vibrational displacement of the Mössbauer nucleus.
my intention is to ask you all about the general details of these moment formula...
may be some of you for sure know about Lipkin'S sum rule.
tha nks

 

[K^2]

So, what is the physical significance of the first and the second moment?

Really?

For starters, <E> is a conserved quantity. ΔE is related to Δt. If this is an energy spectrum of a particle, for example, you just got its mass and half-life.

 

[Dickfore]

general details

Isn't this an oxymoron

 

[K^2]

It's a taxonomy. General details are more specific than detailed generalities, but less specific than plain details.