failure to Integrate in orthogonal polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg67803] failure to Integrate in orthogonal polynomials
- From: Roger Bagula <rlbagula at sbcglobal.net>
- Date: Sat, 8 Jul 2006 04:56:14 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I thought that I might simulate a
one dimensional quantum Legendre system ( particle in a box) in
Mathematica.
It works for odd levels but fails for even levels on the interval/
domain {-1,1}:
p0 = Table[LegendreP[n, x], {n, 1, 5}]
norm = Table[(1/Integrate[p0[[n]]*p0[[n]], {x, -1, 1}])^(1/2), {n, 1, 5}]
p = Table[p0[[n]]*norm[[n]], {n, 1, 5}]
Enm = Table[If[Integrate[p[[n]]*p[[m]], {x, -1,
1}] - 1 == 0, Integrate[p[[n]]*(D[p[[m]], {x,
2}] + 1/x), {x, -1, 1}]/Integrate[p[[n]]*p[[m]], {x, -1, 1}], 0], {n,
1, 5}, {m, 1, 5}]
MatrixForm[Enm]
Inm = Table[N[Integrate[p[[n]]*p[[m]], {x, -1, 1}]], {n, 1, 5}, {m, 1, 5}]
MatrixForm[Inm]
Union[Flatten[N[Enm]]]
If anybody can get an esimate of the even levels it would be nice.
the odd levels are very near +/-Sqrt[6]. I'm using an 1/x potential
function and a second derivative operator.
Roger Bagula