How do I tell Mathematica to reduce trig functions to zero when their arguments are integer multiples of pi or 2pi? I have this:
ψn[x_] := Sqrt[2/a] Sin[(n*Pi*x)/a]
ψl[x_] := Sqrt[2/a] Sin[(l*Pi*x)/a]
Ψbos[x1_,x2_] := (1/Sqrt[2]) (ψn[x1]*ψl[x2] + ψn[x2]*ψl[x1])
Simplify[Integrate[Ψbos[x1, x2]^2*x1^2, {x1, -a, a}],
Assuming l ∈ \[DoubleStruckCapitalZ] && n ∈ \[DoubleStruckCapitalZ]]
When Mathematica finishes this calculation I ran the result through a FullSimplify with same assumptions, but it still gave me terms that should be 0. E.g. there are still terms which involve Sin[2*l*Pi] or Cos[n*Pi] and I don't know how to get Mathematica to make them zero.
Simplify[expr, Assumptions->...]. – Daniel Lichtblau Dec 13 '15 at 21:15Simplify[Integrate[Ψbos[x1, x2]^2*x1^2, {x1, -a, a}], l ∈ Integers && n ∈ Integers]. – Karsten7 Dec 13 '15 at 21:17