From: hackbard Date: Wed, 30 May 2012 07:37:04 +0000 (+0200) Subject: new stuff X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=8e76f77bf1d7e1428796a7cb524a76fd57ca055d;p=lectures%2Flatex.git new stuff --- diff --git a/physics_compact/math_app.tex b/physics_compact/math_app.tex index f1ac777..ec21dae 100644 --- a/physics_compact/math_app.tex +++ b/physics_compact/math_app.tex @@ -165,7 +165,7 @@ u_mv_1^* & u_mv_2^* & \cdots & u_mv_n^*\\ \right) \text{ ,} \end{equation} -which can be equivalently obtained by the rulrs of matrix multiplication +which can be equivalently obtained by the rules of matrix multiplication \begin{equation} \vec{u}\otimes\vec{v}=\vec{u}\vec{v}^{\dagger} \text{ ,} \end{equation} @@ -180,5 +180,47 @@ holds. \section{Spherical coordinates} +Cartesian coordinates $\vec{r}(x,y,z)$ are related to spherical coordinates $\vec{r}(r,\theta,\phi)$ by +\begin{eqnarray} +x&=&r\sin\theta\cos\phi\textrm{ ,}\\ +y&=&r\sin\theta\sin\phi\textrm{ ,}\\ +z&=&r\cos\theta\textrm{ .} +\end{eqnarray} +Infinitesimal translations $dq_i$ and $dq'_i$ of the two coordinate systems are related by the partial derivatives. +\begin{equation} +dq_i=\sum_j \frac{\partial q_i}{\partial q'_j}dq'_j +\end{equation} +\begin{definition}[Jacobi matrix] +The matrix J with components +\begin{equation} +J_{ij}=\frac{\partial q_i}{\partial q'_j} +\end{equation} +is called the Jacobi matrix. +\end{definition} + +For cartesian and spherical coordinates the relation of the translations are presented in detail +\begin{eqnarray} +dx&=&\frac{\partial x}{\partial r}dr + + \frac{\partial x}{\partial \theta}d\theta + + \frac{\partial x}{\partial \phi}d\phi\\ +dy&=&\frac{\partial y}{\partial r}dr + + \frac{\partial y}{\partial \theta}d\theta + + \frac{\partial y}{\partial \phi}d\phi\\ +dz&=&\frac{\partial z}{\partial r}dr + + \frac{\partial z}{\partial \theta}d\theta + + \frac{\partial z}{\partial \phi}d\phi\\ +\end{eqnarray} +and the vector consisting of all or using the Jacobi matrix + + +\begin{equation} + =\sin\theta\cos\phi dr + \\ +\end{equation} + +To obtain infinitesimal +\begin{definition}[Jacobi matrix] + +\end{definition} + \section{Fourier integrals} diff --git a/physics_compact/mech.tex b/physics_compact/mech.tex index e67554c..92f85f0 100644 --- a/physics_compact/mech.tex +++ b/physics_compact/mech.tex @@ -1,2 +1,8 @@ \part{Classical mechanics} +\chapter{Lagrangian mechanics} + +\section{Variational principle} + +\chapter{Theory of relativity} + diff --git a/physics_compact/phys_comp.tex b/physics_compact/phys_comp.tex index 674c88e..7a7d0b2 100644 --- a/physics_compact/phys_comp.tex +++ b/physics_compact/phys_comp.tex @@ -38,7 +38,7 @@ \usepackage{miller} % in use? -\usepackage{slashbox} +%\usepackage{slashbox} % smaller captions ... \usepackage[small,bf]{caption} diff --git a/physics_compact/qm.tex b/physics_compact/qm.tex index bf8b2ee..6b8c6c4 100644 --- a/physics_compact/qm.tex +++ b/physics_compact/qm.tex @@ -49,3 +49,9 @@ Moreover, equality in \eqref{sec:vm_f} is only achieved if $|\tilde 0\rangle$ co \chapter{Quantum dynamics} +\chapter{Relativistic quantum mechanics} + +285 Schulten + + +