Finite Well

Quantum Mechanics · Part 3

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Table of Contents

  1. 1.The Potential
  2. 2.Even and Odd Solutions
  3. 3.Number of Bound States
  4. 4.Scattering States ()
  5. 5.Transmission Coefficient
  6. 6.Key Differences from Infinite Well
  7. 7.Physical Applications
  8. 8.📝 Summary: Finite Square Well

Key Equations

$$V(x) = \begin{cases} -V_0 & |x| < a \\ 0 & |x| > a \end{cases}$$
$$k\cot(ka) = -\kappa$$
$$E_0 \approx -V_0 + \frac{\pi^2\hbar^2}{8ma^2} = -10\,\text{eV} + \frac{\pi^2(1.055 \times 10^{-34})^2}{8(9.11 \times 10^{-31})(10^{-9})^2}$$
$$k_{\text{in}} = \frac{\sqrt{2m(E+V_0)}}{\hbar}, \quad k_{\text{out}} = \frac{\sqrt{2mE}}{\hbar}$$

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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