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

Ron Hardin rhhardin at att.net
Sat Feb 9 10:57:52 CET 2013

```Take an array x(i) of length n with values in -k..k
Take the array of its second differences, y(i)=x(i-1)-2*x(i)+x(i+1), taking x(1)
as circularly adjacent to x(n)
Count the arrays x() that have x(i)*y(j)=y(i)*x(j) for all i and j
(ie, when zero doesn't make it undefined, y(i)/x(i) = some constant E over the
array)
The constant would be an energy eigenvalue.

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

----- Original Message ----
> From: William Keith <william.keith at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, February 8, 2013 8:52:45 PM
> Subject: [seqfan] Re: Time-Indepenent Schrodinger Equation discrete version
>
> On Fri, Feb 8, 2013 at 4:53 PM, Ron Hardin <rhhardin at att.net> wrote:
> >  /tmp/czd
> > T(n,k)=Number of -k..k arrays of length n whose elements are  some constant
>times
> > the end-around second differences
>
> Could you  state your definition more rigorously?  It seems like a
> fairly  non-artificial sort of object and that columns have period 12
> sounds like an  interesting and non-obvious property, but I would like
> to know precisely what  we're looking at.
>
> William  Keith
>
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>
```