Griffiths QM Problem 1.16: Normalization, Expectation Values & Uncertainty | Wave Function

In this video, we solve Problem 1.16 from David J. Griffiths – Introduction to Quantum Mechanics (3rd Edition).
The particle is represented at t = 0 by the wave function
Ψ(x,0) = A(a² – x²) for −a ≤ x ≤ +a, and 0 otherwise.
We compute:
(a) Normalization constant A
(b) Expectation value ⟨x⟩
(c) Expectation value ⟨p⟩
(d) Expectation value ⟨x²⟩
(e) Expectation value ⟨p²⟩
(f) Uncertainty in position σₓ
(g) Uncertainty in momentum σₚ
(h) Verification of the Heisenberg Uncertainty Principle
This problem provides a complete exercise in calculating expectation values, uncertainties, and operator methods in quantum mechanics.
Perfect for BSc/MSc Physics students and anyone preparing for NET / GATE / IIT-JAM.

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Видео Griffiths QM Problem 1.16: Normalization, Expectation Values & Uncertainty | Wave Function канала Vasu V