Sturm Liouville Form. Web it is customary to distinguish between regular and singular problems. Where is a constant and is a known function called either the density or weighting function.
P(x)y (x)+p(x)α(x)y (x)+p(x)β(x)y(x)+ λp(x)τ(x)y(x) =0. We will merely list some of the important facts and focus on a few of the properties. Put the following equation into the form \eqref {eq:6}: Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): P and r are positive on [a,b]. However, we will not prove them all here. 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. We can then multiply both sides of the equation with p, and find. (c 1,c 2) 6= (0 ,0) and (d 1,d 2) 6= (0 ,0); Such equations are common in both classical physics (e.g., thermal conduction) and quantum mechanics (e.g., schrödinger equation) to describe.
The solutions (with appropriate boundary conditions) of are called eigenvalues and the corresponding eigenfunctions. The boundary conditions require that Where α, β, γ, and δ, are constants. We apply the boundary conditions a1y(a) + a2y ′ (a) = 0, b1y(b) + b2y ′ (b) = 0, Where is a constant and is a known function called either the density or weighting function. Such equations are common in both classical physics (e.g., thermal conduction) and quantum mechanics (e.g., schrödinger equation) to describe. Put the following equation into the form \eqref {eq:6}: Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): However, we will not prove them all here. Basic asymptotics, properties of the spectrum, interlacing of zeros, transformation arguments. The solutions (with appropriate boundary conditions) of are called eigenvalues and the corresponding eigenfunctions.
