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Finished the introduction.

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Janita Willumsen
2024-01-01 13:05:09 +01:00
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8
latex/sections/methods.tex
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@@ -6,7 +6,13 @@
% Add something that takes Planck to Schrödinger
% In classical mechanics, we have Newton laws and conservation of energy. In quantum
% mechanics, we have Schrödinger equation.
The Schrödinger equation has a general form
Erwin Schrödinger wanted to find a mathematical description of the wave characteristics
of matter, supporting the wave-particle idea. He postulated a wave function which varies
with position, where the function squared can be interpreted as the probability
of finding an electron at a given position. This resulted in the Schrödinger equation,
a wave eqution of the energy levels for a hydrogen atom. It also shows how a quantum
state evolves with time \cite[p. 81]{wu:2023:quantum}. The Schrödinger equation
has a general form
\begin{align}
i \hbar \frac{\partial}{\partial t} | \Psi \rangle &= \hat{H} | \Psi \rangle \ ,
\label{eq:schrodinger_general}