Recent content by Poirot

Homework Statement A beam of $$^{39}K$$ atoms is slowed with a Zeeman slower with laser light tuned to the $$4s^2S_{1/2} --4p^2P_{3/2}$$ transition with $$F=2, m_F=2 -> F'=3,m_{F'}=3 (\lambda =767nm)$$ Nuclear spin $$I=3/2$$. The most probably velocity the atoms escape from the oven with is...

I'm not testing for equality here, I have an expression that's defined for different values of n which I need to check if (for some values of n) x[n, o] becomes complex, and when this happens I need it to take the negative value of this.

Homework Statement My end goal is to plot null geodesics around a black hole with realistic representations within the horizon (r<2GM, with c=1) using Mathematica. I've done this for outside the horizon using normal Schwarzschild coordinates and gained equation (1) below, and then used this...

I have a Do loop running which, for some values will become complex, and I want to make it so for these situations, we take the negative root and for others the positive root. In this scenario, I've simplified what I actually have and chose to look at the case where I need it to take the...

Thank you for your replies, I found another way of doing this by using the "Do" function and "NSolve", which allowed me to define values outside of the interval I was looking at (which also means I can force it to tail off for large n/-n to make it physically realisable.

Sorry I made a mistake, I meant to say En is set to 10 to ensure non negative for now. This system is actually for an oscillating delta potential $$V(x,t) = s cos(\omega t) \delta(x)$$ and the T I'm looking at here is for the transmission coefficient. n runs from -∞ to ∞ (as a consequence of a...

I am trying to numerically solve the recurrence relation for: $$ T[n]=\frac{sm}{2\hbar^2i k_n}(T[n-1]+T[n+1]) \\ k_n=(\frac{2m(E-\hbar \omega n)}{\hbar^2})^{1/2}$$ My code is: RecurrenceTable[{Tn[ n] == (s* m/(2*\[HBar]^2* I*(2*m*(En -...

I'm also getting an error message every time I run the plot saying "NIntegrate failed to converge to prescribed accuracy after 9 \ recursive bisections in k near {k} = {9.76553}. NIntegrate obtained \ 1.93516*10^-11+1.15758*10^-11\ I and 1.3159348010134315`*^-15 for the \ integral and error...

Thank you so much, this is the most progress I've made in days! It looks like t=7 is towards to end of the animation, and I need to do a bit of tweaking as I think the wave is propagating the wrong way but that should be an easy fix. So can I get Animate to complete the calculations first and...

Ahh brilliant, the check worked, can take values except x=0 which is to be expected. Although when I implement the Animate function, it comes up saying $Aborted which I think may be due to the integral blowing up?

Ahh you're right thank you. Just ran and didn't work however :/.

Ahh I think I see what you mean, I've just given it a go and had a similar error message En = \[HBar]^2*k^2/2*m; Rk = 1/(((\[HBar]^2*I*k)/s*m) - 1); Tk = 1/(1 - (s*m/(\[HBar]^2*I*k))); R = 1/((2*\[HBar]^2*Energy)/(s^2*m) + 1); T = 1/(((s^2*m)/(2*\[HBar]^2*Energy)) + 1); \[HBar] = 1; m = 1; s...

Homework Statement I am trying to solve integrals of the form: ## \int_{-\infty}^{\infty} \frac{k}{k-1} e^{itk^2}e^{ikx}e^{-(k-k_0)^2/\alpha^2} dk \\ \int_{-\infty}^{\infty} \frac{1}{k-1} e^{itk^2}e^{ikx}e^{-(k-k_0)^2/\alpha^2} dk ## A bit of background: I'm trying to create an animation in...

I have tried NIntegrate and I get an error " "The integrand \[Psi][x,t,k] has evaluated to non-numerical values \ for all sampling points in the region with boundaries \ {{-\[Infinity],0.}}" Which is think is due to the integral containing x and t in the exponents (which aren't to be integrated...

I'm trying to use the Animate function on Mathematica to show a gaussian wave packet passing through a delta potential. I'm quite new to Mathematica and this is by far the hardest thing I've had to do so please bear with me. I effectively want to solve the integral: ## \phi_k(x) = \left\{...