Hilbert Spaces
Quantum Mechanics · Part 1
188 KB10 sections4 key equationsLaTeX typeset
Table of Contents
- 1.1.1 Vector Spaces Over ℂ
- 2.1.2 Inner Product
- 3.1.3 Cauchy-Schwarz Inequality
- 4.Definition: Vector Space
- 5.Examples of Vector Spaces
- 6.Definition: Inner Product
- 7.Examples of Inner Products
- 8.The Norm
- 9.Proof Sketch
- 10.Key Concepts (Page 1)
Key Equations
$$|\psi\rangle = \begin{pmatrix} \psi_1 \\ \psi_2 \\ \vdots \\ \psi_n \end{pmatrix}, \quad \psi_i \in \mathbb{C}$$
$$\langle \psi | \alpha\phi + \beta\chi \rangle = \alpha \langle \psi | \phi \rangle + \beta \langle \psi | \chi \rangle$$
$$\langle \psi | \phi \rangle = \sum_{i=1}^n \psi_i^* \phi_i$$
$$|\langle \psi | \phi \rangle|^2 \leq \langle \psi | \psi \rangle \langle \phi | \phi \rangle$$
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 ...