Subject: Maxima can't solve this integral equation
From: Richard Hennessy
Date: Tue, 24 Jun 2008 23:27:08 -0400
Made a mistake.
The answer should be
E[n] = (%pi/C*mu^(1/4)*hbar/sqrt(2*m)*(n-1/2))^(4/3)
Rich
------------Original Message------------
From: "Richard Hennessy"<rvh2007 at comcast.net>
To: "Maxima List" <maxima at math.utexas.edu>
Date: Tue, Jun-24-2008 11:06 PM
Subject: Maxima can't solve this integral equation
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?
Rich