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Quantum Mechanics · Part 2

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Table of Contents

  1. 1.Statement
  2. 2.Ehrenfest's Theorem
  3. 3.WKB Approximation
  4. 4.Classical Limit Conditions
  5. 5.Example: Harmonic Oscillator

Key Equations

$$\frac{d\langle\hat{x}\rangle}{dt} = \frac{\langle\hat{p}\rangle}{m}, \quad \frac{d\langle\hat{p}\rangle}{dt} = -\left\langle\frac{\partial V}{\partial x}\right\rangle$$
$$\psi(x) \approx \frac{C}{\sqrt{p(x)}}e^{i S(x)/\hbar}$$
$$|\psi_n(x)|^2 \xrightarrow{n\to\infty} \frac{1}{\pi\sqrt{A^2 - x^2}} \quad \text{(classical PDF)}$$

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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