How to use Maple to solve equation normalization coefficient

user_18719067 0
Viewed 56

I want to ask for the normalization coefficient of the solution f(x).

The implementation method in Mathematica is as follows:

f[x] := Sin[(n Pi x)/(2 a)];
norm = FullSimplify[1/Integrate[Abs[f[x]]^2, {x, 0, a}], n \[Element] Integers]

The final results are as follows: 2/a

I want to implement the same function in Maple, and have tried the following：

assume(n::posint);
psi := x -> sin(1/2*n*pi*x/a);
c := 1/int(abs(psi(x))^2, x = 0 .. a);
simplify(solve(c = 1, a));

Is there a good way to deal with it if it is implemented with Maple?

maple
1 Answers
restart;

kernelopts(version);

   Maple 2022.0, X86 64 LINUX, Mar 8 2022, Build ID 1599809

assume(n::posint);
f := abs(sin(1/2*n*Pi*x/a))^2:

simplify(combine(1/int(convert(f,Heaviside,x),
                       x=0..a)));

        2
        -
        a

simplify(combine(1/int(f,x=0..a)))
   assuming a::real;

        2
        -
        a
user_3385600
Related