डिफरेंशियल ऑपरेटर L | ग्रीन का फलन G | अनुप्रयोग के उदाहरण |
---|
 |  | |
 |  | |
 |  | |
where  | with  | 1D underdamped harmonic oscillator |
where  | with  | 1D overdamped harmonic oscillator |
where  |  | 1D critically damped harmonic oscillator |
2D Laplace operator  | with  | 2D Poisson equation |
3D Laplace operator  | with  | Poisson equation |
Helmholtz operator  |     | stationary 3D Schrödinger equation for free particle |
in dimensions |  | Yukawa potential, Feynman propagator |
 |  | 1D wave equation |
 |  | 2D wave equation |
D'Alembert operator  |  | 3D wave equation |
 |  | 1D diffusion |
 |  | 2D diffusion |
 |  | 3D diffusion |
 | with  | 1D Klein–Gordon equation |
 | with  | 2D Klein–Gordon equation |
 | with  | 3D Klein–Gordon equation |
 | with  | telegrapher's equation |
 | with  | 2D relativistic heat conduction |
 | with  | 3D relativistic heat conduction |