So for the phase velocity of a massive particle we have
Vph = Vg/2 for non-relativistic case
Vph = c^2/Vg for the relativistic case
Vg is the group velocity or particle velocity
But there seems to be a contradiction in that for the non-relativistic case the phase velocity is...
Im trying to make a buffer for tubulin and using circular dichroism - I just need the buffer to be ~ pH 7.4 and to be transparent in the 185-240nm region. This mono/dibasic potassium phosphate buffer does this but seems needlessly complicated. Would monobasic potassium phosphate with sodium...
Thanks, that makes some sense. But now wouldn't we be caught in a catch 22; we need the concentrations to figure out the ionic strength but then we also need the ionic strength to figure out the concentrations from the altered pKa and HH equation. This got complicated real quickly.
I don't have...
So I want to make a Potassium Phosphate Buffer from monobasic and dibasic forms of potassium phosphate because it was recommended for doing circular dichroism scans due to its low absorption in the UV region. However I don't understand the proportions of mono basic and dibasic forms of potassium...
Ok thanks. This is the only axiom of inner products that bothers me. So we could define the inner product of a complex vector space as
<v,u> = v1u1 + v2u2 + v3u3
with no complex conjugates but we would lose some nice properties that are convenient such as length?
What is the motivation behind defining the inner product for a vector space over a complex field as
<v,u> = v1*u1 + v2*u2 + v3*u3
where * means complex conjugate
as opposed to just
<v,u> = v1u1 + v2u2 + v3u3
They both give you back a scalar. The only reason I can see is the special case for...
Homework Statement
Show that the pressure of a solid is given by
P = -\frac{\partial\Phi_0}{\partial V} + \gamma \frac{U}{V}
\Phi_0(V) is the potential energy of the solid when all atoms are at rest in their equilibrium positions and V is the volume of the solid.
U is the internal energy...
Homework Statement
For an ideal Bose gas in a uniform gravitational field, at what temperature does Bose-Einstein condensation set in. Gas is in a container of height L.Homework Equations
Normal BEC temperature of an ideal Bose gas not under the influence of gravity is
T = \frac{h^2}{2 \pi m...
To solve the the blackbody radiation Planck had to solve the partition function or average energy for a harmonic oscillator. But where did he get the inspiration to change the energy of the harmonic oscillator from E = \frac{1}{2} m v^2 + \frac{1}{2} k x^2 to simply E = n h v
This seems like...
Can we take the grand canonical ensemble and then switch the roles of the thermodynamic conjugate variable pair (P, V) making P (pressure) the parameter and V (volume) the variable and allowing it to fluctuate in the system. The macrostate would then be defined by the pressure temperature and...
How do you invert a series? Can't find any information on it.
I need to invert a function and solve for z in powers of x
x = \sum_{n=1}^\infty\\b_n z^n
I'm guessing we can just say
z = \sum_{n=1}^\infty\\a_n x^n
But if this is right I don't know why its right or if it can be...
How many permutations (when objects are not all distinct) of size k can be created from a set of size N composed of n1, n2,n3,...,nr parts?
When k = N this is easy and is equal to N!/(n1!n2!...nr!)
The following question would be then how many combinations (when objects are not all distinct)...