Homework Statement
A Hydrogen atom is interacting with an EM plane wave with vector potential
$$\bar A(r,t)=A_0\hat e e^{i(\bar k \cdot \bar r -\omega t)} + c.c.$$
The perurbation to the Hamiltonian can be written considering the proton and electron separately as...
Which books/resources would you recommend to study superfluidity for a 3rd year undergrad seminar?
It needs to focus on phenomenology rather than technical details. Assume some QM background, but before a first course on condensed matter. Thanks!
Is there a good description or formula regarding how the sound pressure from a constant source depends upon ambient pressure?
That is, if I were to conduct an experiment where I put a source and a microphone in a container, and then change the pressure in that container with a pump, assuming...
Homework Statement
Let ##\left|\psi\right\rangle## be a non-degenerate stationary state, i.e. an eigenstate of the Hamiltonian. Suppose the system exhibits symmetry for time inversion, but not necessarily for rotations. Show that the expectation value for the angular momentum operator is zero...
Homework Statement
What are the electric and magnetic fields due to a charge that is moving with uniform acceleration?
(Non relativistic)
Homework Equations
Retarded solutions for the vector and scalar potentials.
The Attempt at a Solution
My attempt might be an overkill because I'm using the...
Homework Statement
Let $$\vec H = ih_4^{(1)}(kr)\vec X_{40}(\theta,\phi)\cos(\omega t)$$
where ##h## is Hankel function of the first kind and ##\vec X## the vector spherical harmonic.
a) Find the electric field in the area without charges;
b) Find both fields in a spherical coordinate system...
Thanks for your replies!
I managed both (a) and (b) and understood its underlying principles. I'm now left with (c).
We were suggested to define ##\phi = |\psi_0|## where ##\psi_0## is the wave function of the ground state, and then express ##\phi## in terms of the Hamiltonian eigenvectors and...
Homework Statement
Assume a particle with a wave function ##\psi(x)## such that ##-\infty < x < \infty##, that move under some potential ##V(x)##.
Show that:
a) two wave functions with same energies can only differ by a complex phase;
b) if the potential is real, then you can choose the wave...
Homework Statement
Let ##f## be a bounded function on ##[0,1]##. Let ##P_n## be a partition of ##[0,1]## such that ##P_n = (0,\frac{1}{n},\frac{2}{n},...,1)##. Finally, we define ##\alpha=\inf\{U(f,P_n):n\geq1\}##, where ##U(f,P)## is the upper Darboux sum of ##f## with partition ##P##.
Show...
Homework Statement
An infinite plane in z=0 is held in potential 0, except a square sheet -2a<x,y<2a which is held in potential V.
Above it in z=d there is a grounded plane. Find:
a) the potential in 0<z<d?
b) the total induced charge on the z=0 plane.
Homework Equations
Green's function for a...
Homework Statement
An infinite plane in z=0 is held in potential 0, except a square sheet -2a<x,y<2a which is held in potential V.
Above it in z=d there is a grounded plane. Find:
a) the potential in 0<z<d?
b) the total induced charge on the z=0 plane.
Homework Equations
Green's function for a...
Homework Statement
A wave with an initial profile ##U(z)=Ae^{ik_0z}e^{-\frac{z^2}{2\sigma^2}}## is traveling in the z direction (yes, the Gaussian profile and the optical axis are not perpendicular). It then passes through a prism with apex angle ##\alpha## and refractive index...
Ok, got it, it indeed doesn't matter- we can decompose the expression for the y component and take the real part.
One last thing, I didn't understand your discussion of the dot products. Is there anything wrong with how I calculated the coefficients?
Ok, we can solve for them by
$$
\begin{pmatrix}1\\
0
\end{pmatrix}=\frac{c_{l}}{\sqrt{2}}\begin{pmatrix}1\\
i
\end{pmatrix}+\frac{c_{r}}{\sqrt{2}}\begin{pmatrix}1\\
-i
\end{pmatrix}\Rightarrow c_{l}=c_{r}=\frac{1}{\sqrt{2}}$$
and now
$$
\mathbf{E} =...
Yes, the vectors are ##\frac{1}{\sqrt 2}(1,-i), \frac{1}{\sqrt 2}(1,i)## for circularly polarized light, and (a,b) for some linear polarization.
But I'm not sure how the initial linear input should be written.
I thought that if ## E_0 = E_{x0} \hat x ## then
$$\frac{1}{\sqrt 2}E_{x0}...