I am ultimately trying to get Mathematica to solve some equations which are related to a tunnelling problem with an oscillating delta potential.(adsbygoogle = window.adsbygoogle || []).push({});

I have the coefficients for absorption and emission:

$$ T_n = \frac{sm}{i\hbar^2} (T_{n-1} + T_{n+1})$$

$$T_q = \frac{sm}{2ik_q \hbar^2} (T_{q-1} +T_{q+1}) +1$$

where $$k_{q/n} =(\frac{2m(E-\hbar \omega q(or \ n))}{\hbar^2})^{1/2}$$

So I'm trying to do this for a finite number of n, such as -2 to 2, and have given the seed values T[-2]=T[2]=1 (as far as I'm aware these can be whatever I want).

I've tried using RSolve but it just pops out the input again as the output, and also won't allow me to specify the particular range for n. I was told that RSolve probably won't be able to do this as they "won't have a closed form" and so to use the "Do" function. I tried this but all it spits out is the 5 equations for n=-2,-1... 2 etc and doesn't solve them.

I'm setting all the constants out the front to 1. For some context, I'm trying to build a programme that shows a gaussian wave packet entering a delta potential which is oscillating in strength ($$V(x) =\delta(x) scos(\omega t)$$) and the initial wave is monochromatic (which gives the transmission coefficient Tq, taking q to be effectively anything). The Tn part is from the Fourier transform that allows all n not equal to q which has no incident part, only reflection and transmission (I'll deal with the reflection once I get somewhere with the transmission).

Any help would be very much appreciated, I'm quite a newbie with Mathematica and even the physics is beyond me for the most part.

Thanks!

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# Mathematica Solving recurrence equations in QM tunneling example

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