# A Potential Energy Curve for Ammonia Inversion?

1. Apr 22, 2016

### kq6up

For my Quantum II class I am working on a paper about masers. I am using a naive model (a coupled pair of infinite potential wells), and I would like to find out where I can find a graph of the inversion potential energy curve. This would be a simple one dimensional curve of the potential along the Nitrogen inversion axis. If one googles Ammonia maser, a qualitative curve can easily be found, but I have been unsuccessful in finding a graph that actually has data points on it. A set of points would be fine too. My end game is using this data to find the partition size in the middle. I am going to use a potential energy partition for the wells that has a full maximum values but the width set at half the height of the real curve. The solution for my model is the value of the wave number $k$ for a pair of transcendental equations that have a family of roots where n=1,2,3, etc. The $k$'s can be use to calculate the transition energy between even and odd parity states, and hopefully this energy will be somewhat closely correspond to a 24GHz frequency , and hopeWhat numerical calculation function would be best for finding roots of transcendentals involving trig and hyperbolic trig functions?

Thanks,
KQ6UP

2. Apr 22, 2016

### A. Neumaier

The built-in ones in the programming languague you are using. There is nothing special about transcendentals. If the functions are wiggly you may need several starting points to find all the roots (or even one).

For finding the data go back to early papers on the subject and look at what they used. Or find a reasonably recent paper and write a polite email to its youngest author.

3. Apr 22, 2016

### kq6up

I was planning on just using Mathematica. Is #FindRoot a good one?

Thanks,
KQ6UP

4. Apr 22, 2016

### A. Neumaier

You can check by creating some test functions of the kind you will need, plot them, and visually check whether the output of #FindRoot matches your requirements.

5. Apr 22, 2016

### kq6up

Perfect, thank you.

KQ6UP

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