Question Bank MCQ • 2 Marks Section 1: Mathematical Physics Differential equations

QB_PH_013: Differential equations

Question Statement

The Green's function $G(x, x')$ for the differential operator $\frac{d^2}{dx^2}$ satisfies which derivative jump condition at $x = x'$?
(A) \left.\frac{dG}{dx}\right|_{x'+} - \left.\frac{dG}{dx}\right|_{x'-} = 1
(B) \left.\frac{dG}{dx}\right|_{x'+} - \left.\frac{dG}{dx}\right|_{x'-} = 0
(C) G(x'+, x') - G(x'-, x') = 1
(D) \left.\frac{dG}{dx}\right|_{x'+} - \left.\frac{dG}{dx}\right|_{x'-} = -1
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Integrating $\frac{d^2G}{dx^2} = \delta(x - x')$ across the singularity gives jump of $+1$.
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