Adiabatic

Quantum Mechanics · Part 6

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Table of Contents

  1. 1.Statement of the Adiabatic Theorem
  2. 2.Quantifying "Slow": The Adiabaticity Condition
  3. 3.The Dynamic Phase
  4. 4.The Geometric (Berry) Phase
  5. 5.Berry Connection and Berry Curvature
  6. 6.Example: Particle in an Expanding Box

Key Equations

$$\hat{H}(t)|n(t)\rangle = E_n(t)|n(t)\rangle$$
$$\left|\frac{\langle m(t)|\dot{\hat{H}}(t)|n(t)\rangle}{(E_n(t) - E_m(t))^2/\hbar}\right| \ll 1 \quad \text{for all } m \neq n$$
$$\boxed{\theta_n(t) = -\frac{1}{\hbar}\int_0^t E_n(t')\, dt'}$$
$$\boxed{\gamma_n = i\oint_{\mathcal{C}} \langle n(\vec{R})|\vec{\nabla}_R|n(\vec{R})\rangle \cdot d\vec{R}}$$

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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