I am trying to solve the following equation.
m\frac{du}{dt}=-\gamma u -\frac{dV}{dx} + A(t)
Where u is the momentum, x is position, V is the external potential dependent on position, and A is the random stochastic force dependent on time. There is no initial condition in this problem, but...
Homework Statement
So I'm trying to evaluate the following integral:
4\pi r^2{\int_0}^\infty r^2\frac{\sin{sr}}{sr}dr
which after canceling out one of the r's, gives an integral similar to that of xsinx.
I need to show that this integral vanishes for all values of s that are not 0...
I had a math question about the following steps.
The Shroedinger's equation can be written as follows.
\LARGE i\hbar \frac{d}{dt}U(t) |\psi(0)> = HU(t)|\psi(0)>
Where H is the hamiltonian and U is the time evolution operator.
So U satisfies the schrodinger equation.
\LARGE...
fixed it
For particle location, perturbation theory, etc, I see the following integral.
\LARGE \int_0^t { e^{i\omega t^'}}dt^'
Where \omega is some constant, or frequency. It says in my text that this is equal to 0 if \omega is not close to 0. My logic leads me to think that when...
For particle location, perturbation theory, etc, I see the following integral.
\LARGE \int_0^t { e^{i\omega t^'}}dt^'
Where \omega is some constant, or frequency. It says in my text that this is equal to 0 if \omega is not close to 0. My logic leads me to think that when \omega is...
For particle location, perturbation theory, etc, I see the following integral.
\LARGE \int_0^t { e^{i\omega t^'}}dt^'
Where \omega is some constant, or frequency. It says in my text that this is equal to 0 if \omega is not close to 0. My logic leads me to think that when \omega is...
I think I figured out the problem. Hopefully I didn't make any huge mistakes.
Consider an isolated volume partitioned by a moveable impermeable membrane.
\LARGE V_{total} = V_A + V_B
since total volume is constant
\LARGE (1) \hspace*{5mm} dV_A = -dV_B
We can write the total...
Yes, this is true for ideal gases, and probably in general that the negative of the compressibility is positive. But this is based on empirical evidence of positive pressure. Of course there are meta stable systems with negative pressure, but not for true equilibrium. This seems good enough...
I have a question on the quantity -(dV/dP)T,N where V = volume, P = pressure, T = temp, N = number of moles and T, N are held constant. I see in textbooks that this quantity is always positive at equilibrium. It makes intuitive sense, as if it were negative, it would be unphysical. I've been...