Question Bank MCQ • 1 Mark Section 1: Mathematical Physics Fourier and Laplace transforms

QB_PH_008: Fourier and Laplace transforms

Question Statement

The Fourier transform $\int_{-\infty}^\infty e^{-a x^2} e^{-ikx} dx$ (with $a > 0$) is proportional to:
(A) e^{-k^2 / (4a)}
(B) e^{-k^2 / (2a)}
(C) e^{-a k^2}
(D) \frac{1}{k^2 + a^2}
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Complete the square in the exponent: $-ax^2 - ikx = -a(x + ik/2a)^2 - k^2/4a$.
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