Question Bank MCQ • 2 Marks Section 4: Quantum Mechanics Schrodinger equation

QB_PH_098: Schrodinger equation

Question Statement

The probability current density for a stationary plane wave $\psi(x) = A e^{ikx}$ is:
(A) \frac{\hbar k}{m} |A|^2
(B) 0
(C) \frac{\hbar k^2}{2m} |A|^2
(D) \frac{\hbar}{m} |A|^2
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $J = \frac{\hbar}{2mi}(\psi^* \nabla \psi - \psi \nabla \psi^*) = \frac{\hbar k}{m}|A|^2$.
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