27 lines
1.9 KiB
TeX
27 lines
1.9 KiB
TeX
% !TeX root = ../script.tex
|
|
\documentclass[../../script.tex]{subfiles}
|
|
|
|
\begin{document}
|
|
\chapter{Fundamentals of Quantum Physics}
|
|
\minitoc
|
|
\vspace*{\fill}\par
|
|
\pagebreak
|
|
|
|
Due to the uncertainty principle, location and impulse of an atomic particle cannot be both stated with arbitrairy precision.
|
|
The classic trajectory, represented in the model of mass points by a well-defined curve in space $\vec{r}(t)$, is replaced by the probability
|
|
\begin{equation}
|
|
W(x, y, z, t) \dd{v} = \abs{\psi(x, y, z, t)}^2 \dd{V}
|
|
\end{equation}
|
|
to find the particle in the volume element $\dd{V} = \dd{x}\dd{y}\dd{z}$ at the time $t$. This probability depends on the absolute square of the matter wave function $\psi(x, y, z, t)$.
|
|
|
|
In this chapter we wnat to show how this wave function can be calculated for simple examples. These examples will also demonstrate the physical fundamentals of quantum mechanics and its
|
|
differences to classical particle mechanics, elaborate on the concept of \textit{quantum numbers} and show under which conditions quantum mechanical results can be transitioned into classical physics.
|
|
This is supposed to clarify that classic (i.e.\ pre-quantum) mechanics are contained in quantum mechanics as a limiting case for very small de Broglie wavelengths $\lambda_{dB} \rightarrow 0$.
|
|
|
|
These examples should also demonstrate that almost all insights of quantum mechanics are already known in classic wave optics. This means: the actual novel concepts in quantum mechanics
|
|
is the description of classic particles with matter waves. The deterministic description of the temporal development of location and impulse of a particle is thus replaced with a statistical
|
|
treatment, by which we can only discuss probabilities of the results of a measurement. A fundamental uncertainty occurs when we observe location and impulse at the same time.
|
|
|
|
\subfile{schroedinger.tex}
|
|
\subfile{examples.tex}
|
|
\end{document} |