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--- models:basic_models:harmonic_oscillator [2018/03/27 14:58]
jakobadmin [Intuitive]
+++ models:basic_models:harmonic_oscillator [2018/06/06 10:35] (current)
jakobadmin
@@ Line 1: / Line 1: @@
+<WRAP lag>$ L= \frac{ \color{blue}{m}}{2} \left( \color{olive}{\frac{dx}{dt}}\right)^2 - \frac{ \color{red}{k}}{2} \color{magenta}{x}^2$</WRAP>
 ====== Harmonic Oscillator ======
@@ Line 5: / Line 7: @@
 {{ :hookeslaw.png?nolink&300|}}
+A harmonic oscillator simply consists of an object attached to a spring and is one of the simplest physical systems we can study.
+To describe the system we usually track the $\color{magenta}{\text{position}}$ of the object at the end of the spring. The continuous up and down movement is called an oscillation, which is where the name "oscillator" comes from.
+The movement depends crucial on the $\color{red}{\text{properties of the spring}}$. When the spring is harder, the movements of the object will be smaller. In addition, the motion of the object depends on its $\color{blue}{\text{mass}}$. A heavier object will perform larger swings.
 <tabbox Concrete>
-  * A good description can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf
+  * A good description of the harmonic oscillator in quantum mechanics can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf
@@ Line 15: / Line 22: @@
 <tabbox Abstract>
+The [[basic_tools:phase_space|phase space]] of a harmonic oscillator
+{{ :basic_tools:phasespaceoscillator.png?nolink&600 |}}
 <tabbox Why is it interesting?>
@@ Line 44: / Line 54: @@
 <tabbox FAQ>
---> Why do we introduce the ladder operators?#
+--> Why do we introduce the ladder operators to treat the harmonic oscillator in quantum mechanics?#
     * See https://behindtheguesses.blogspot.de/2009/03/quantum-harmonic-oscillator-ladder.html

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