Talk:Sturm separation theorem

Assessment comment
Substituted at 02:36, 5 May 2016 (UTC)

Critique of proof
This proof of the theorem is faulty. The statement "Since u and v are linearly independent it follows that the Wronskian W[u,v] must satisfy W[u,v](x) != 0 for all x where the differential equation is defined" is not correct. The Wronskian can be zero at a finite number of points, it just cannot be zero everywhere. Take for example, the time-independent Schrodinger equation with an infinite square well, V(x) = 0 on 0<x<&pi;, &infin; elsewhere. The solutions u(x)=sin(x) and v(x)=sin(3x) are clearly linearly independent, but their Wronskian is zero in the middle of the well at x=&pi;/2. Other parts of the proof fall apart after this, but I wanted to make sure I did not misunderstand some of the assumptions here before proposing a major rewrite of this page. Rjones30 (talk) 14:19, 18 July 2017 (UTC)