Green's Function (ODE Form)

Source lecture(s): PHY621 Lec7

Physical Meaning

Impulse response of a linear differential operator.

Variable Definitions

Symbol	Meaning
\(G(x;x_0)\)	Green's function
\(\delta\)	Dirac delta source

Assumptions

Linear operator; homogeneous boundary conditions.

Derivation

Construct from two independent homogeneous solutions matched at \(x_0\) with slope discontinuity \(1/W\).

Applications

Poisson equation, wave scattering, quantum propagators.

Connections to Other Equations

• partial-differential-equations
• ordinary-differential-equations