[seqfan] Re: Time-Indepenent Schrodinger Equation discrete version

Ron Hardin rhhardin at att.net
Wed Feb 20 18:42:21 CET 2013


That's a great find!

I'm not sure how it applies here (geometry doesn't seem to figure in the same 
way).

My feeling is that if you can get a set of n sines for some n and offset, even 
if they're all irrational but in rational ratios to each other, then you can use 
a big enough k to multiply up the common ratio denominator and get an all 
integral solution outside the 1,2,3,4,6 restriction.

Physically, adding enough energy to uncover rare cases.

But perhaps I'm not seeing the strength of the restriction.

 rhhardin at mindspring.com
rhhardin at att.net (either)



----- Original Message ----
> From: L. Edson Jeffery <lejeffery2 at gmail.com>
> To: seqfan at list.seqfan.eu
> Sent: Wed, February 20, 2013 1:53:32 AM
> Subject: [seqfan] Re: Time-Indepenent Schrodinger Equation discrete version
> 
> >Is https://oeis.org/A219844
> 
> >Calculated as many T(n,k) terms as I  can and they agree with the empirical
> >formula.
> 
> >The formula  though obviously depends on a fact about sampling x(j)  of
> >sin(j*2Pi/n+offset), namely that you can't find a set of x(j) with  
>exclusively
> >rational ratios except for n=1,2,3,4 or 6.
> 
> >I don't  know how you'd go about proving that.
> 
> 
> 
> As for proving the fact, is  it not already known as the "crystallographic
> restriction?"
> 
> Ed  Jeffery
> 
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