Scattering

Quantum Mechanics · Part 3

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Table of Contents

  1. 1.General Scattering Setup
  2. 2.Square Barrier
  3. 3.Tunneling Time
  4. 4.Resonant Tunneling
  5. 5.Double Barrier & Quantum Wells
  6. 6.WKB Approximation for Tunneling
  7. 7.Physical Applications
  8. 8.Gamow Factor
  9. 9.📝 Chapter Summary

Key Equations

$$\psi(x) = \begin{cases} Ae^{ikx} + Be^{-ikx} & x < 0 \quad \text{(incident + reflected)} \\ Ce^{iqx} + De^{-iqx} & 0 < x < a \quad \text{(inside barrier)} \\ Fe^{ikx} & x > a \quad \text{(transmitted)} \end{cases}$$
$$\kappa = \frac{\sqrt{2m(V_0 - E)}}{\hbar} = \frac{\sqrt{2(9.11\times10^{-31})(10-5)(1.6\times10^{-19})}}{1.055\times10^{-34}}$$
$$T \approx e^{-2\kappa a}, \quad \kappa = \frac{\sqrt{2m(V_0 - E)}}{\hbar}$$
$$\frac{\sqrt{2m(E-V_0)}}{\hbar} \cdot a = \pi$$

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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