Harmonic Oscillator
Quantum Mechanics · Part 3
206 KB5 sections4 key equationsLaTeX typeset
Table of Contents
- 1.The Hamiltonian
- 2.Algebraic Method: Ladder Operators
- 3.Energy Eigenvalues & Eigenstates
- 4.📝 Chapter Summary
- 5.Interactive Simulation
Key Equations
$$V(x) = \frac{1}{2}m\omega^2 x^2$$
$$\hat{H} = \frac{\hat{p}^2}{2m} + \frac{1}{2}m\omega^2\hat{x}^2$$
$$E_n = \hbar\omega\left(n + \frac{1}{2}\right), \quad n = 0,1,2,\ldots$$
$$E_0 = \frac{(1.055 \times 10^{-34})(8.28 \times 10^{14})}{2} = 4.37 \times 10^{-20}\,\text{J}$$
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 ...