models:basic_models:harmonic_oscillator
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models:basic_models:harmonic_oscillator [2017/10/22 17:29] jakobadmin [Student] |
models:basic_models:harmonic_oscillator [2018/06/06 10:35] (current) jakobadmin |
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| + | <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> | ||
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| ====== Harmonic Oscillator ====== | ====== Harmonic Oscillator ====== | ||
| - | <tabbox Why is it interesting?> | + | |
| + | <tabbox Intuitive> | ||
| + | {{ :hookeslaw.png?nolink&300|}} | ||
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| + | A harmonic oscillator simply consists of an object attached to a spring and is one of the simplest physical systems we can study. | ||
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| + | 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. | ||
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| + | 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. | ||
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| + | <tabbox Concrete> | ||
| + | * 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 | ||
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| + | <tabbox Abstract> | ||
| + | The [[basic_tools:phase_space|phase space]] of a harmonic oscillator | ||
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| + | {{ :basic_tools:phasespaceoscillator.png?nolink&600 |}} | ||
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| + | <tabbox Why is it interesting?> | ||
| <blockquote>“The career of a young theoretical physicist consists of treating the harmonic | <blockquote>“The career of a young theoretical physicist consists of treating the harmonic | ||
| oscillator in ever-increasing levels of abstraction.” <cite>Sidney Coleman</cite></blockquote> | oscillator in ever-increasing levels of abstraction.” <cite>Sidney Coleman</cite></blockquote> | ||
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| + | <blockquote>In a sense, the harmonic oscillator is to physics what the set of natural numbers | ||
| + | is to mathematics. It is a simple, almost “trivial” system, but one which conceals | ||
| + | much subtlety and beauty and from which a great deal of what is of interest in the | ||
| + | subject evolves. <cite>[[http://gregnaber.com/wp-content/uploads/Simple-Harmonic-Oscillator.pdf|Gregory L. Naber]]</cite></blockquote> | ||
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| <cite>[[http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf|The Simple Harmonic Oscillator]] by F. Porter</cite></blockquote> | <cite>[[http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf|The Simple Harmonic Oscillator]] by F. Porter</cite></blockquote> | ||
| - | <tabbox Layman> | ||
| - | <note tip> | ||
| - | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | ||
| - | </note> | ||
| | | ||
| - | <tabbox Student> | ||
| - | * A good description can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf | ||
| + | | ||
| + | <tabbox FAQ> | ||
| - | **FAQ:** | + | --> Why do we introduce the ladder operators to treat the harmonic oscillator in quantum mechanics?# |
| - | * Why do we introduce the ladder operators? | ||
| * See https://behindtheguesses.blogspot.de/2009/03/quantum-harmonic-oscillator-ladder.html | * See https://behindtheguesses.blogspot.de/2009/03/quantum-harmonic-oscillator-ladder.html | ||
| - | <tabbox Researcher> | ||
| - | <note tip> | ||
| - | The motto in this section is: //the higher the level of abstraction, the better//. | ||
| - | </note> | ||
| - | |||
| - | --> Common Question 1# | ||
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| <-- | <-- | ||
| - | --> Common Question 2# | ||
| - | |||
| - | <-- | ||
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| - | <tabbox Examples> | ||
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| - | --> Example1# | ||
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| - | <-- | ||
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| - | --> Example2:# | ||
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| - | |||
| - | <-- | ||
| - | | ||
| - | <tabbox History> | ||
| </tabbox> | </tabbox> | ||
models/basic_models/harmonic_oscillator.1508686173.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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