[Maxima-commits] CVS: maxima/share/orthopoly variational_method.dem, 1.3, 1.4

[Barton W. <wil...@us...>]

Update of /cvsroot/maxima/maxima/share/orthopoly
In directory sc8-pr-cvs16.sourceforge.net:/tmp/cvs-serv20818/share/orthopoly

Modified Files:
	variational_method.dem 
Log Message:
o Append another demo  of a variational method.

Index: variational_method.dem
===================================================================
RCS file: /cvsroot/maxima/maxima/share/orthopoly/variational_method.dem,v
retrieving revision 1.3
retrieving revision 1.4
diff -u -d -r1.3 -r1.4
--- variational_method.dem	23 Dec 2005 13:46:58 -0000	1.3
+++ variational_method.dem	12 May 2008 17:16:34 -0000	1.4
@@ -89,3 +89,25 @@
 remfunction(ham,"<<",f);
 remvalue(n,psi,vars,min_this,eqs,m_det,solve_ord,pows,unks,eq,ans);
 assume_pos : false;
+
+
+/* Let's apply a variational method to the potential x^2 / 2 + x^4. We'll assume
+a trial wavefuction of the form qo * exp(-%alpha * abs(x)^(2*n) / 2) where the
+parameters are %alpha and n. See "Post-Gaussian variational method for quantum anharmonic
+oscillator," by Akihiro Ogura." */
+
+kill(all)$
+assume(qo > 0, %alpha > 0, n > 1/2)$
+f : qo * exp(-%alpha * abs(x)^(2*n) / 2);
+1 = integrate(f^2,x,minf,inf);
+solve(%,qo);
+f : subst(second(%), f);
+v : x^2 / 2 + x^4$
+ham(f) := -diff(f,x,2) / 2 + v * f$
+energy : integrate(f * ham(f),x,minf,inf);
+eqs : [diff(energy,n), diff(energy,%alpha)]$
+load(mnewton)$
+newtonepsilon : 1.0e-15$
+sol : mnewton(eqs,[n,%alpha],[1.1, 2.0]);
+subst(sol, energy);
+