Recent content by skynelson

Hi, I'm teaching Engineering (honors) and want to drill the students on series, parallel resistors in circuits and voltage dividers. does anybody a have a worksheet with lots of samples? Thanks!

Thank you @WernerQH that's an interesting set of ideas. By the way, here is a sample problem in an anonymous textbook that gave me the indication that this problem could be addressed in some standard way by undergraduates. See the "Exercise" at the bottom. The solutions we've come to so far...

It is not helpful to quote an obvious result with no clarification on how to apply it to the given use case.

Hi Jambaugh, yes, that makes some sense...not that I am particularly good at contour integrals but I do understand a bit about why it would be useful in this case, since your exponents are not purely real or purely imaginary. You've also implicitly answered that to your knowledge this is not a...

Note that the first order solution is simply ##\int_{-\infty}^{\infty} dt_1 e^{i \omega_{10}t_1} e^{-t_1^2/2\tau^2} = e^{-\tau^2 \omega_{10}^2/2}##

Consider the gaussian kick potential, ##\hat{V}(t) = \hat{x} \exp{(\frac{-t^2}{2 \tau^2})}## where ##\hat{x} = a+a^\dagger## in terms of creation and annihilation operators. Then we define the potential in the interaction picture, ##\hat{V}_I(t) = e^{i\hat{H}t}\hat{V}(t)e^{-i\hat{H}t}## I...

Hi Jason, Thanks for the clarification. I included some working code below that illustrates what I was trying to accomplish. My research project is formulating the Time Dependent Schrodinger Equation perturbation series in terms of recursive convolutions. I haven't found a resource for this, so...

Thanks hdp12 for the response! This is a good approach for more specific control over layout.

Yes, That's it! And yes, MATLAB. I figured there was a straightforward syntactical approach. Thanks Jason.

I want my graph to display the tick values along the x-axis, instead of the index number. Because I use linspace, my data goes from 0 to 1, but my index ranges from 1 to 1000. My plot labels the x-axis from 1 to 1000, by default. I want to change the default (or just program it) to display 0 to...

Thank you both! Your explanations clear up my thinking. Starting from where you left off, Jason, I now want to create a smooth version of ##\mathcal{F}(\omega)## by performing ideal interpolation (convolution with a sinc function): $$\mathcal{F}_{\text{~smooth}} = sinc(\omega T) \ast...

Hello, I've read that repeated convolution tends, under certain conditions, to Gaussian distribution. I found this description helpful, and Wikipedia's version of this says: The central limit theorem states that if x is in L1 and L2 with mean zero and variance ##σ^2##, then...

Thanks Vanhees71, it's great to see this example worked out, fascinating. Can you tell me more about this quantity, $$\alpha \equiv \vec{A}_0 \cdot <E,t_0|\hat{\vec{p}}(t_0)|E, t_0>$$ for the non time-dependent amplitude is the part I am having some trouble gaining an intuition for. I...

Thanks for the very clear description, jambaugh. So it looks like we picked eigenfunctions of a convenient scenario (square well) even though they weren't eigenfunctions of the actual potential, which included a square well plus a perturbation ##V(x)##. Right? And it's because of that we end up...

Thank you, I'll check it out!