Wave Functions

Quantum Mechanics · Part 2

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Table of Contents

  1. 1.Position Representation
  2. 2.Probability Interpretation
  3. 3.Momentum Representation
  4. 4.Schrödinger Equation in Position Space
  5. 5.Probability Current & Continuity
  6. 6.Properties of Wave Functions
  7. 7.📝 Chapter Summary

Key Equations

$$\psi(\vec{r},t) = \langle \vec{r}|\psi(t)\rangle$$
$$A^2\int_0^L \frac{1 - \cos(2\pi x/L)}{2}dx = 1$$
$$\tilde{\psi}(\vec{p},t) = \frac{1}{(2\pi\hbar)^{3/2}}\int e^{-i\vec{p}\cdot\vec{r}/\hbar}\psi(\vec{r},t)d^3r$$
$$\phi(p) = \frac{A}{\sqrt{2\pi\hbar}}\sqrt{2\pi\sigma^2}e^{-p^2\sigma^2/2\hbar^2}$$

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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