Uncertainty

Quantum Mechanics · Part 2

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Table of Contents

  1. 1.General Uncertainty Relation
  2. 2.Position-Momentum Uncertainty
  3. 3.Energy-Time Uncertainty
  4. 4.Minimum Uncertainty States
  5. 5.Interpretation: Fundamental, Not Observational
  6. 6.Summary

Key Equations

$$\Delta A \cdot \Delta B \geq \frac{1}{2}|\langle[\hat{A},\hat{B}]\rangle|$$
$$|\langle\hat{A}\hat{B}\rangle|^2 \geq \left|\frac{1}{2}\langle[\hat{A},\hat{B}]\rangle\right|^2$$
$$E \sim \frac{(\Delta p)^2}{2m} = \frac{(5.25 \times 10^{-25})^2}{2 \times 9.11 \times 10^{-31}}$$
$$\Delta f = \frac{\Delta E}{h} = \frac{\Delta E}{2\pi\hbar} = \frac{1}{2\pi\tau}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...

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