I'm working in Liboff, 4e, QM, page 114, problem 4.35.
An electron in a 1-D box with walls at x= 0,a is in the state \psi(x) = A for x\in (0,a/2) and \psi(x) = -A for x\in (a/2,a). What is the lowest possible energy that can be measured?
From my understanding, the answer to this question...
I take \textbf{r}(t,u)=t(\cos u,\sin u,1) to be a parametrization of the cone. The norm of the fundamental vector product is (this can be easily checked)
\| \frac{\partial \textbf{r} }{\partial u} \times \frac{\partial \textbf{r} }{\partial t} \| = \sqrt{2} t
As you can tell by my...
We have a right circular cone of base radius a and height a with a uniform surface charge sigma. I want to determine the potential difference between the apex of the cone and the center of the base (this cone doesn't have any charge on the base).
My plan of attack for the problem was to...
Yes, I got something similar to that. I was working out a problem where the point was to show that things get too messy when you try to get a solution directly. But that recursion formula seems just fine to me.
That's what I originally thought too.
Here's our equation:
\frac{d^2\psi}{du^2}+(\frac{\beta}{\alpha}-u^2)\psi=0
This is the SE for the simple harmonic oscillator. My text goes through an elaborate solution to this DE and ends up resorting to a power series solution, not for psi, but for H, where \psi=H(u)e^{-u^2/2}. The text...
\displaystyle e=\sum \limits_{n=0}^{\infty} \frac{1}{n!}, if I remember correctly.
What are you interested in learning about series?
Most series, as far as I know, don't have names.
Your initial condition y(0)=2 seems to imply that c = 0, not -1=1?
You can preclude y=-2 simply by noticing that it fails to satisfy the initial condition.
The capacitance will of course cancel since we are given no information about the capacitor itself.
The energy store in a capacitor is U = \frac{1}{2} CV^2.
The problem at hand states \frac{1}{2} C_1V_1^2= \frac{1}{2} C_2V_2^2. You are looking for V_2.
For the third one, http://www.sengpielaudio.com/calculator-ohm.htm.
Your first question is unclear.
For the second one, can you tell me the energy in the capacitor without the dielectric? Qualitatively, do you expect the required voltage to be more or less than the case with k=1?
Do you have...