When we talk about a two-state quantum system being a two-dimensional complex Hilbert space are we implicitly considering the "existence of time"? Why is all this additional structure (of a two-dimensional complex Hilbert space) necessary if, even with a full quantum mechanical perspective...
Okay, thanks! I'll look into direct and indirect band gaps!
Also, I have another related question. When the P-type material and the N-type material are fused into the PN-junction, does combination happen close to where the two materials were fused together? That would create some sort of gap...
In a pure crystal structure of some semiconductor compound each molecule is usually bound to other four by covalent bonds, in other words each of the four valence electrons of each molecule is in a covalent bond with another molecule. At 0K all electrons remain in these covalent bonds, but as...
I was actually wondering about the rate of conversion between amplitudes and frequencies of sound waves and electric signals when the conversion is done by a dynamic microphone. Like if I was talking in a certain frequency with a certain amplitude into one of these microphones what would be the...
Can I get the voltage generated by a vibrating coil around a magnet as a function of the frequency and amplitude of the vibration (given all necessary informations about the coil and magnet)? What would that function be? Also, what information about the coil and magnet would be sufficient and...
Yes, ##i\pi## lies within the contour, which means that the integral for any closed path around ##i\pi## would wield the right answer, but that didn't help me much. I still don't know how to calculate the integral.
Homework Statement
Calculate the complex integral along the closed path indicated:
$$ \oint_C\frac{\sin{z}}{z^2+\pi^2}dz,\,\,|z-2i|=2.$$
Homework Equations
$$ \sin{z}=\frac{e^{iz}-e^{-iz}}{2i} $$
$$ e^{iz}=e^{i(x+iy)}=e^{-y+ix}=e^{-y}(\cos{x}+i\sin{x}) $$
The Attempt at a Solution
I really...
In complex analysis differentiability for a function ##f## at a point ##z_0## in the interior of the domain of ##f## is defined as the existence of the limit
$$ \lim_{h\rightarrow{}0}\frac{f(z_0+h)-f(z_0)}{h}.$$
But why are the possible ##z_0##'s in the closure of the domain of the original...
When studying the motion of particles in space, what are the mathematical considerations that have to made of spacetime? Could I say there exists a bijection between spacetime and ##\mathbb{R}^4##? Is the topology under consideration the usual product topology of ##\mathbb{R}^4##? Are there any...
I used the Frobenius method on ##R##, which gives the answer as a power series of that form. But I honestly don't know what the next step is, after I found ##Z(z)=A(e^{kz}-e^{-kz})## I don't know what to do.
I still don't see what the next step is.. How do I keep solving the problem from here?
I'm not sure.. Are you talking about
R(r)=\sum_{n=0}^\infty{}b_n(rk)^{n+m},
the solution for the Bessel equation? Which would mean that
\sum_{n=0}^\infty{}b_n(ak)^{n+m}=0.
Is that what I am supposed to...
Thanks! Already fixed the typo.
Could you expand on that?
The condition ##Z(0)=0## implies that ##A=-B##, right?. Do I use ##R(a)=0## before ##Z(L)=u_0##? And does that mean that I would have to solve Bessel's equation to completely solve this problem?
Homework Statement
A hollow cylinder with radius ##a## and height ##L## has its base and sides kept at a null potential and the lid on top kept at a potential ##u_0##. Find ##u(r,\phi,z)##.
Homework Equations
Laplace's equation in cylindrical coordinates...
Homework Statement
A bar of length ##L## has an initial temperature of ##0^{\circ}C## and while one end (##x=0##) is kept at ##0^{\circ}C## the other end (##x=L##) is heated with a constant rate per unit area ##H##. Find the distribution of temperature on the bar after a time ##t##.
Homework...