Subject: Maxima can't solve this integral equation
From: Raymond Toy
Date: Wed, 25 Jun 2008 16:44:09 -0400
Richard Hennessy wrote:
> Hi,
>
> (%i3) integrate(sqrt(2*m*(E[n]-mu*x^4)),x,-a[0],a[0])=(n-1/2)*%pi*hbar
>
> It gives just the noun form.
>
> But if you do the following substitution manually it can be done.
>
> z=(mu/E[n])^(1/4)*x
>
> You should get an answer after solving for E[n] of
>
> E[n] = %pi/C*mu^(1/4)*hbar/sqrt(2*m)*(n-1/2)
>
> where C can be computed numerically from
>
> (%i4) quad_qags(sqrt(1-z^4), z, -1, 1);
>
> Is this a bug or is it the way I am formulating the problem?
>
>
Not sure if it's a bug, but there is some information missing. I don't
see how, from your original integral with limits +/- a[0], you can use
your substitution to get an integral from -1 to 1. In any case your
integral is an elliptic integral, and Maxima doesn't know anything
about elliptic integrals. (I have some really hackish code to teach
maxima a little about elliptic integrals, but it's not very complete nor
well thought out.)
Ray