theories:classical_theories
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| ====== Classical Theories ====== | ====== Classical Theories ====== | ||
| - | <tabbox Why is it interesting?> | + | <tabbox Overview> |
| + | Classical theories are useful approximations of [[theories:quantum_theory|quantum theories]] for objects that are large. | ||
| - | Classical theories are useful approximations of quantum theories. | + | <nspages theories:classical_theories -h1 -textPages=""> |
| - | <tabbox Layman> | + | ---- |
| + | [{{ :theories:classicaltheories.png?nolink&800 |Source: http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/1201.1.K.pdf}}] | ||
| - | <note tip> | + | <tabbox History> |
| - | 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> | + | |
| - | <note tip> | + | * For a nice overview, see the [[https://en.wikipedia.org/wiki/Timeline_of_classical_mechanics|timeline of classical mechanics at Wikipedia]]. |
| - | In this section things should be explained by analogy and with pictures and, if necessary, some formulas. | + | * https://golem.ph.utexas.edu/category/2008/01/a_tiny_taste_of_the_history_of.html |
| - | </note> | + | |
| - | + | ||
| - | <tabbox Researcher> | + | |
| - | <note tip> | ||
| - | The motto in this section is: //the higher the level of abstraction, the better//. | ||
| - | </note> | ||
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| - | <tabbox Examples> | ||
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| - | --> Example1# | ||
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| - | <-- | ||
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| - | --> Example2:# | ||
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| - | <-- | ||
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| - | <tabbox FAQ> | ||
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| - | --> How can we understand the transition from quantum to classical physics?# | ||
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| - | For a nice discussion, see chapter 2 in Sleeping Beauties in Theoretical Physics by Thanu Padmanabhan: | ||
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| - | "Particles do not follow trajectories. They are described by | ||
| - | wavefunctions but under appropriate circumstances the constructive interference | ||
| - | of the phases of the wavefunction will single out a path which | ||
| - | we call a classical trajectory. The [[equations:hamilton-Jacobi_equation]] is just the | ||
| - | lowest-order Schrodinger equation if we use the ansatz in Eq. (2.1). The ¨ | ||
| - | mysterious procedure in Hamilton-Jacobi theory — of differentiating the | ||
| - | solution to Hamilton-Jacobi equation and equating it to a constant — is | ||
| - | just the condition for constructive interference of the phases of waves | ||
| - | differing slightly in the parameter E. The procedure based on Hamilton-Jacobi | ||
| - | theory works in [[theories:classical_theories:classical_mechanics|classical mechanics]] because it is supported by the | ||
| - | [[equations:schroedinger_equation|Schrodinger equation]]" | ||
| - | |||
| - | <-- | ||
| - | | ||
| - | <tabbox History> | ||
| </tabbox> | </tabbox> | ||
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