Thank you for pointing out my abuse of notation, in treating the general momentum operator and its real-space representation as the same. I had been thinking of the derivative as the momentum operator. When editing the question to fix my notation, I realized my error. I have edited the question...
Suppose we have a Hamiltonian containing a term of the form
where ∂=d/dr and A(r) is a real function. I would like to study this with harmonic oscillator ladder operators. The naïve approach is to use
where I have set ħ=1 so that
This term is Hermitian because r and p both are.*...
Thanks, everyone!
Baluncore: Wow, I must have missed that. Thanks for pointing it out!
LvW: Whoops, sorry about the typo. Yes, we only used the linear approximation in the class I took - we didn't need anything finer at the time. I appreciate your contribution!
Svein and donpacino: Thanks for...
If you're referring to the Taylor expansion, this site provides several good reasons and examples. The reasons they list are approximations of all sorts, series solutions of differential equations, and limiting values.
Are there simple governing equations for FETs like there are for BJTs, and if so, what are they? For example, in the BJT case we have
IC = β×IB
IE + IC + IB
I'm sure it depends on the type - MOSFET, JFET, etc. - so anything anyone could contribute would be helpful. From what I understand, the...
Hey, I have only a little experience with electronics, and I'm looking for a simple sensor for a magnetometer sensitive enough to detect about a gauss and accelerometer for detecting when something is picked up. As long as I can get a good explanation (data sheets can sometimes be cryptic) I'd...
I've got a Green's function in which all the impulses are on the line from the north pole to the origin (polar angle θ=0) and terminating with a point impulse at the north pole. I've found its gradient at a field point, and I want to rotate everything to a new coordinate system with the source...
Thank you all! I found these as well:
http://isthis4real.com/orbit.xml
https://dan-ball.jp/en/javagame/planet/
I should have been more specific about the nature of the demos - they should be accessible to all ages and require less than a minute of instruction to begin and take no longer than a...
Thank you for anything you can offer. We've got a plasma globe which we can tie into talking about solar and interstellar plasma, and we have a few Galileoscopes, but we don't really have anything else astronomy-themed. I've been thinking, but haven't come up with many ideas.
One idea I did...
I have a very rudimentary multimeter; it won't check AC voltages this low. I considered that the 555 might be busted by static, so I tried with a Wein bridge oscillator - no good there either. However, I know for a fact that the LM741 I'm using is working. That's only supposed to put out 25 mA -...