3d Schrodinger

Quantum Mechanics · Part 4

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Table of Contents

  1. 1.Time-Independent Schrödinger Equation
  2. 2.Cartesian Coordinates
  3. 3.Spherical Coordinates
  4. 4.Separation of Variables
  5. 5.3D Infinite Box
  6. 6.Momentum Operators
  7. 7.Free Particle in 3D
  8. 8.Probability Current Density

Key Equations

$$-\frac{\hbar^2}{2m}\nabla^2\psi(\vec{r}) + V(\vec{r})\psi(\vec{r}) = E\psi(\vec{r})$$
$$x = r\sin\theta\cos\phi, \quad y = r\sin\theta\sin\phi, \quad z = r\cos\theta$$
$$\psi_{n_x,n_y,n_z}(x,y,z) = \left(\frac{2}{L}\right)^{3/2}\sin\left(\frac{n_x\pi x}{L}\right)\sin\left(\frac{n_y\pi y}{L}\right)\sin\left(\frac{n_z\pi z}{L}\right)$$
$$[\hat{x}_i, \hat{p}_j] = i\hbar\delta_{ij}$$

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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