What Does $$E^2_k|_{k=k_{res}}$$ Mean?

  • Thread starter Thread starter NODARman
  • Start date Start date
  • Tags Tags
    Physic Symbol
NODARman
Messages
57
Reaction score
13
Homework Statement
.
Relevant Equations
.
Hi, just wondering what this thing means.
$$
E^2_k|_{k=k_{res}}
$$
Just the k=k(res) after the vertical line. There is no definition in the textbook but in math does that mean from K=K(res) to something that can be dependent on a function or a situation?

Like definite integrals answer $$x|^3_2=3-2=1$$
 
Physics news on Phys.org
NODARman said:
Homework Statement:: .
Relevant Equations:: .

Hi, just wondering what this thing means.
$$
E^2_k|_{k=k_{res}}
$$
Just the k=k(res) after the vertical line. There is no definition in the textbook but in math does that mean from K=K(res) to something that can be dependent on a function or a situation?

Like definite integrals answer $$x|^3_2=3-2=1$$
Without additional context it's hard to say. However, I don't think it's like a definite integral. Can you post a clear picture of the textbook page where this appears?
 
$$
\left(\begin{array}{c}
D_{\psi \psi} \\
D_{\psi p}=D_{p \psi} \\
D_{p p}
\end{array}\right)=\left(\begin{array}{c}
\left.D \frac{\delta}{\gamma^2} E_k^2\right|_{k=k_{\text {res }}} \\
-\left.D \frac{\psi m c}{\gamma} E_k^2\right|_{k=k_{\text {res }}} \\
\left.D \frac{\psi^2 m^2 c^2}{\delta} E_k^2\right|_{k=k_{\text {res }}}
\end{array}\right),
\space where \space
E_k^2=\hbar \omega(k) n(k)=\int \frac{k^2 d \Omega}{(2 \pi)^2} \hbar \omega(\mathbf{k}) n(\mathbf{k})
$$
is energy density per unit of a one-dimensional wave vector and we assumed that ω(k) is an isotropic function of k.
we know that k is a wave vector (and the index "res" could be a doppler resonance for short) but what does it mean in that context (with E^2)?

This is from synchrotron radiation texbook.
Mark44 said:
Without additional context it's hard to say. However, I don't think it's like a definite integral. Can you post a clear picture of the textbook page where this appears?
I'll try to find the book.
 
NODARman said:
Hi, just wondering what this thing means.
$$
E^2_k|_{k=k_{res}}
$$
It means ##E^2_k## evaluated at ##k=k_{res}##.
 
  • Like
Likes Grelbr42, PhDeezNutz, PeroK and 1 other person
##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
Back
Top