I'm currently carrying out an analysis on waveforms produced by a particular particle detector. The Nyquist-Shannon sampling theorem has been very useful for making an interpolation over the original sample points obtained from the oscilloscope. The theorem (for a finite set of samples) is given...
I only have a doubt about which definition to use for the multiplicity of a two state system. Clearly the total multiplicity of a two state system is given by:
Ω=2^N,
but what about the definition:
Ω(N,n) = \binom{N}{n} = \frac{N!}{n!\cdot(N-n)!}.
Clearly:
2^N ≠...
This is the problem:
Consider a system of two Einstein solids, with NA = 300, NB = 200, and qtotal = 100. Compute the entropy of the most likely macrostate and of the least likely macro state.
I only have a doubt. Is the most likely macro state when each solid has half the energy (in this...
The problem asked me to prove the following (where \vec{r}, \vec{v}, \vec{a} are the position, velocity and acceleration vectors of a moving particle):
\frac{d}{dt} [\vec{a} \cdot (\vec{v} \times \vec{r})] = \dot{\vec{a}} \cdot (\vec{v} \times \vec{r})
I already did so, but my question...
I'm given the position vector as a function of time for a particle (b, c and ω are constants):
\vec{r(t)} = \hat{x} b \cos(ωt) + \hat{y} c \sin(ωt)
To obtain it's velocity i differentiate \vec{r(t)} with respect to time and i obtain:
\vec{v(t)} = -\hat{x} ωb \sin(ωt) + \hat{y} ωc...