Recent content by lampCable

Letting ##g=Ax+B## and ##h=Cx+D##, and inserting the ansatz into the equation we find ##\phi '' = (A-C)\delta(x) + (B-D)\delta'(x) = -q\delta \Rightarrow A = -q+C,\ B = C##. So it does indeed follow that ##g = (-q+C)x + D## and ##h = Cx + D##. This shows that ##\phi\to D## in the limit as...

How did you know that ##\phi## was continuous at ##x=0##?

Okay, so if I use the first approach and integrate again I get for ##x<0## that ##\phi = -qx + Ax + B## and for ##x>0## that ##\phi = Ax + C##. But can I really use a continuity argument at ##x=0## to conclude that ##B = C##?

Homework Statement Solve ##\Delta\phi = -q\delta(x)## on ##\mathbb{R}##. Correct answer: ##\phi = -\frac{q}{2}|x| + Ax + B## Homework EquationsThe Attempt at a Solution In one dimension the equation becomes ##\frac{d^2 \phi}{d x^2} = -q\delta(x)##. We integrate from ##-\infty## to ##x## to...

Have you considered the torque about point B?

Homework Statement Consider an aircraft turbine as in the figure below. In the reference frame of the turbine, air of density ##\rho_0## comes into the turbine with speed ##U_0## through the entrance with cross sectional area ##S_0##. In the combustion zone, air is mixed with the fuel and...

Turns out that the answer to this question was simple. The charge density at any point is ##\rho=e(p+N_D-n-N_A )##. But as I mentioned in the question, in the depletion layer ##n=p=0##. And on the p side we have ##N_D=0## since there are no donor atoms there, which gives ##\rho=-eN_A##...

Homework Statement In an abrupt p-n junction we consider the junction between one side p-doped with ##N_A## acceptor atoms and another side n-doped with ##N_D## donor atoms. Initially the chemical potential is different in the two sides, but thermal equilibrium requires that the chemical...

I see. But the Boltzmann distribution is only related to the translational degrees of freedom, so if we talk about fluctuations in say rotational energy then how is that described?

Okay, I think I understand. So when we talk about fluctuations in energy of a single particle in the system, we essentially talk about fluctuations in speed of that particle?

Homework Statement Consider an ensamble of particles that can be only in two states with the difference ##\delta## in energy, and take the ground state energy to be zero. Is it possible to find the particle in the excited state if ##k_BT=\delta/2##, i.e. if the thermal energy is lower than the...

Okay, so I think I have found the answer, and I thought that I'd share it in case anyone else has the same question. Maybe the question was a bit unclear, but what I didn't understand was essentially how we used the "single-particle state" to define the system. So we're considering a system...

Homework Statement I'm trying to understand a derivation of the Fermi-Dirac and Bose-Einstein distributions. In my textbook Thermal Physics by D. V. Schroeder it says: "The idea is to first consider a "system" consisting of one single-particle state, rather than a particle itself. Thus the...

So the system is found either occupied or unoccupied with the probabilities ##P(H)## or ##P(H^+)##, respectively. If we then consider ##N## such systems we should find that there are ##N(H) = P(H)N## occupied states and ##N(H^+)=P(H^+)N## unoccupied states, so that...

Homework Statement Consider a system consisting of a single hydrogen atom/ion, which has two possible states: unoccupied (i.e., no electron present) and occupied (i.e., one electron present, in the ground state). Calculate the ratio of the probabilities of these two states, to obtain the Saha...