Time Independent
Quantum Mechanics · Part 6
212 KB8 sections4 key equationsLaTeX typeset
Table of Contents
- 1.The Setup
- 2.The Unperturbed Problem
- 3.The Perturbation Series Expansion
- 4.Deriving the Corrections
- 5.First-Order Energy Correction
- 6.First-Order State Correction
- 7.Second-Order Energy Correction
- 8.Validity Conditions
Key Equations
$$\hat{H} = \hat{H}_0 + \lambda\hat{H}'$$
$$E_n = E_n^{(0)} + \lambda E_n^{(1)} + \lambda^2 E_n^{(2)} + \lambda^3 E_n^{(3)} + \cdots$$
$$\lambda^0: \quad \hat{H}_0|n^{(0)}\rangle = E_n^{(0)}|n^{(0)}\rangle$$
$$\lambda^2: \quad \hat{H}_0|n^{(2)}\rangle + \hat{H}'|n^{(1)}\rangle = E_n^{(0)}|n^{(2)}\rangle + E_n^{(1)}|n^{(1)}\rangle + E_n^{(2)}|n^{(0)}\rangle$$
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 ...