OK, so you mean the pressure due to the weight of water contained at the z part (##\rho g h_{z}##) will act also along the right side affecting the area ##A_{y}## hence its force = ##\rho g h_{z} A_{y}##, am I correct in this interpretation.
the confusing thing also is, if I use integration it...
Hi All, in the following problem:
the book solution
I don't understand why he added the term
$$
\rho g h_{z} A_{y}
$$
shouldn't it just be :
$$
F = 1/2 \rho g h_{y} A_{y}
$$
the paper isn't open access so I thought I would write the question separably, here is the link of the paper:
the paper, the commutation relation is included in the paper but i am not interested in proving them, rather my concern is equations 4a,4b,4c
Hi all
I found this expression in a paper that concerns the derivation of some relations about boson operators but it is not very clear to me how the results were obtained. The derivation starts as, let B be an operator as a linear combination of different boson operators:
$$...
hi all
I am trying to install the ARPACK library for windows (another program needs the library for calculations) , I download a arpack96.tar.gz file that i found online , downloaded "make" and the mingw-gfortran and all that, modified the ARmake and the Makefile, but when i try the command...
Hi all
I am trying to follow a derivation of something involving second quantization formalism, I am stuck at this step :
$$
\sum_{m2}\sum_{\mu1}
\bra{2,m1,2,m2}\ket{k,q}\bra{2,\mu1,2,\mu2}\ket{k,-q}\delta_{-m2,\mu1}
= (-1)^{2+m2}\frac{\sqrt{2k+1}}{\sqrt{5}}\bra{k,-q,2,m2}\ket{2,-m1}\times...
hi all
how do I prove that
$$
<A^{n}>=<A>^{n}
$$
It seems intuitive but how do I rigorously prove it, My attempt was like , the LHS can be written as:
$$
\bra{\Psi}\hat{A}.\hat{A}.\hat{A}...\ket{\Psi}=\lambda^{n} \bra{\Psi}\ket{\Psi}=\lambda^{n}\delta_{ii}=\lambda^{n}
$$
and the RHS equal:
$$...
Hi all
I am a little bit confused about the definition of angular frequency in the context of nuclear rotation, some times its defined in the regular way as
$$
E=\hbar \omega
$$
and other time from the rigid rotor formula
$$
E=\frac{\hbar^{2}}{2I} J(J+1)
$$
where ##I## is the moment of inertia...
##y## is the measured data
##\tilde{y}## is the calculated data from a specific model
##\delta y_i ## is the error in measuring ##y##
##m## the number of parameters of the model
I am not talking about the so called category chi2. I mean the other one
Hi all
I want to calculate the reduced Chi square and root mean square deviation RMSD of some data points that i have, but I am confused about the correct formula for each of them, which one is the correct one. I found this formula in a paper where they referred to it as the RMSD :
$$...
the idea is that I want to determine the values of k,c for the specific model given by ##y=kx/(5+cx)##, because I will use the formula of the model in further calculations. from what I unstrood from you guys now I believe that the person who told me that the parameters vary could be mistaken or...