## 593 Reputation

16 years, 238 days

## Algebraic formulation...

I am keeping things incredibly simple. The problem is - if things are too simple, classical mechanics predicts electrons and protons collapse. Of course, we know by quantum mechanics that they do not - that there exist minimal distances between them. I crudely use this as a boundary condition on the distances between particles.

I am making a static model - as if the electrons and atomic nuclei simply "hang there" in space, with absolute knowledge of their positions - in complete violation of Heisenberg's Uncertainty Principle.  So, no time derivative.

I am working on 2 electrons and 2 atomic nuclei right now: a tetrahedron. I am trying to prove that their configuration ought to be planar - in order to keep the 2 electrons as far apart from one another as possible and the atomic nuclei as far apart from one another.

On wikipedia, I found the determinantal formula for the volume of a tetrahedron - given the lengths of its 6 edges.  If one chooses the 6 lengths arbitrarily in such a way that this formula yields a negative value, then no such tetrahedron with those edge lengths exist.  The volume =0 is the degenerate / critical / boundary case.

I cannot really make use of calculus (derivative = 0) to find the minimum value of the total potential energy of this system

A point in my network is either an electron or an atomic nucleus.

E = sum over i<j of Zi*Zj*ei*ej/rij where Zi = atomic number (Zi=1 for an electron), ei=e if an electron, ei=-e if an atomic nucleus

## Procedures...

Thanks, Alex Smith! But, the output of your code seems to be just the code itself. However, thank you for introducing me to a new set of commands Procedures. I will have many questions very soon about that.

## Thank you!...

I always had Document Mode and Worksheet Mode backwards. I had always assumed I was working in Worksheet Mode when I found out I had been in Document Mode all along.

## How do I display "X = " X output on a si...

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## How do you make a new line without execu...

How were you able to write code with line breaks something 1; something 2; something 3; without setting off the execution mode in Maple after hitting the Enter key? Please let me know, as this will be very useful to me. Also, where is the Units template? I use the Help menu all the time. But, to assign units to a variable, they ask me to go to the Units template. But, I do not see the Units template on the Worksheet. Thanks.

## Never mind! I figured it out on my own!...

That's always the best way to get a problem solved, anyway. Too bad (yes, I am being superstitious) that figuring out a problem on my own comes only after I beg the entire world for an answer. Turns out I was simply making wrong assumptions. Given a partition A of N, for most (random) choices of another partition B of N, there does NOT exist a domino tabloid of shape A of type B. The parts of B have to be parts of a (sub)partitions of each part of A. Plus, I was confusing a "tabloid" with a "tableaux". My bad. Ian Grant Macdonald is the only person on earth, it seems, who can help me with this stuff. I wish I could become an expert on his book all by myself, just by doing the examples. I'm just not self-disciplined enough, so it seems. I need to use all this theory all the time. In case anyone else is curious, here's what I got. Let z^n + (-1)^(n-s)*e(n-s)*z^s + (-1)^n*e(n) be trinomial in z. e(n-s) = the n-s-th elementary symmetric function in this trinomial's roots. e(n)= the n-th elementary symmetric function of the roots. Let p(m)= the m-the powersum of the roots. m is a positive integer, with p(0)=n. Then p(m)= the sum of (((a+b)-choose-a)*n - ((a+b-1)-choose-b)*s) times ((e(n-s))^a )*((e(n))^b) * ((-1)^(m-a-b)) over all nonnegative integers a and b such that a*(n-s)+b*n = m. This is a "one-dimensional" sum, due to the condition a*(n-s)+b*n = m on a and b. One can replace b with (m - a*(n-s))/n and add the condition "sum over all nonnegative integers, a, such that (m - a*(n-s))/n is a nonnegative integer".