Sturm Liouville Form. The solutions (with appropriate boundary conditions) of are called eigenvalues and the corresponding eigenfunctions. Such equations are common in both classical physics (e.g., thermal conduction) and quantum mechanics (e.g., schrödinger equation) to describe.
Share cite follow answered may 17, 2019 at 23:12 wang The boundary conditions require that P and r are positive on [a,b]. All the eigenvalue are real For the example above, x2y′′ +xy′ +2y = 0. P, p′, q and r are continuous on [a,b]; Where is a constant and is a known function called either the density or weighting function. There are a number of things covered including: Where α, β, γ, and δ, are constants. We just multiply by e − x :
The boundary conditions require that There are a number of things covered including: P, p′, q and r are continuous on [a,b]; P and r are positive on [a,b]. The functions p(x), p′(x), q(x) and σ(x) are assumed to be continuous on (a, b) and p(x) >. Put the following equation into the form \eqref {eq:6}: However, we will not prove them all here. (c 1,c 2) 6= (0 ,0) and (d 1,d 2) 6= (0 ,0); Web so let us assume an equation of that form. All the eigenvalue are real Web solution the characteristic equation of equation 13.2.2 is r2 + 3r + 2 + λ = 0, with zeros r1 = − 3 + √1 − 4λ 2 and r2 = − 3 − √1 − 4λ 2.
