
Recent Posts
Recent Comments
 Determinants II: Determinants of Order $n$  MathPhys Archive on Determinants I: Determinants of Order 2
 Inverses  MathPhys Archive on The Matrix Associated with a Linear Map
 The Matrix Associated with a Linear Map  MathPhys Archive on Linear Maps
 Introduction to Topology 3: Limit Points, Boundary Points, and Sequential Limits  MathPhys Archive on Introduction to Topology 1: Open and Closed Sets
 Parallel Transport, Holonomy, and Curvature  MathPhys Archive on Line Bundles
Archives
Categories
 Algebraic Topology
 Calculus
 Classical Differential Geometry
 College Algebra
 Differential Equations
 Differential Geometry
 Electromagnetism
 Engineering Mathematics
 Functions of a Complex Variable
 General Topology
 Homology
 Lie Groups and Lie Algebras
 Linear Algebra
 Mathematical Physics
 Partial Differential Equations
 Precalculus
 Quantum Mechanics
 Representation Theory
 Sage
 Trigonometry
 Uncategorized
Meta
Monthly Archives: April 2012
Quantum Angular Momentum in $\mathbb{R}^{2+2}$ and $\mathfrak{su}(1,1)$ Representation
It can be shown that quantum angular momentum \begin{align*} L_x&=i\hbar\left(y\frac{\partial}{\partial z}z\frac{\partial}{\partial y}\right)\\ L_y&=i\hbar\left(z\frac{\partial}{\partial x}x\frac{\partial}{\partial z}\right)\\ L_z&=i\hbar\left(x\frac{\partial}{\partial y}y\frac{\partial}{\partial x}\right) \end{align*} can be obtained purely mathematically by $\mathfrak{su}(2)$ Lie algebra representation as discussed here. Since $\mathfrak{su}(2)$ representation contains information on the symmetry … Continue reading
Quantum Angular Momentum and $\mathfrak{su}(2)$ Representation
In classical mechanics, the angular momentum of a body is given by $$L=r\times p$$ where $r$ and $p$ denote radius arm and linear momentum respectively. In quantum mechanics, the angular momentum of a spinning particle can be obtained by replacing … Continue reading