## How do you solve the Sturm-Liouville problem?

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These equations give a regular Sturm-Liouville problem. Identify p,q,r,αj,βj in the example above. y(x)=Acos(√λx)+Bsin(√λx)if λ>0,y(x)=Ax+Bif λ=0. Let us see if λ=0 is an eigenvalue: We must satisfy 0=hB−A and A=0, hence B=0 (as h>0), therefore, 0 is not an eigenvalue (no nonzero solution, so no eigenfunction).

## What is a Sturm-Liouville eigenvalue problem?

The problem of finding a complex number µ if any, such that the BVP (6.2)-(6.3) with λ = µ, has a non-trivial solution is called a Sturm-Liouville Eigen Value Problem (SL-EVP). Such a value µ is called an eigenvalue and the corresponding non-trivial solutions y(.; µ) are called eigenfunctions.

**How do you find the eigenvalues in Sturm-Liouville?**

(p(x)y′)′ + (q(x) + λr(x))y = 0, a < x < b, (plus boundary conditions), is called an eigenfunction, and the corresponding value of λ is called its eigenvalue. The eigenvalues of a Sturm-Liouville problem are the values of λ for which nonzero solutions exist.

**What is Sturm-Liouville differential equation?**

In mathematics and its applications, classical Sturm–Liouville theory is the theory of real second-order linear ordinary differential equations of the form: (1) for given coefficient functions p(x), q(x), and w(x) and an unknown function y of the free variable x.

### What is a regular Sturm-Liouville problem?

on an interval [a, b] is a SL differential equation. are called periodic boundary conditions. with p(x) > 0 and ω(x) > 0 for x ∈ [a, b] is called as regular Sturm-Liouville system (or problem). yλ and its derivative are continuous on [a, b], which also means these are bounded.

### What is eigenvalue Schrodinger equation?

The term eigenvalue is used to designate the value of measurable quantity associated with the wavefunction. If you want to measure the energy of a particle, you have to operate on the wavefunction with the Hamiltonian operator (Equation 3.3. 6).