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theories:quantum_mechanics:path_integral [2018/05/06 11:50] jakobadmin [Concrete] |
theories:quantum_mechanics:path_integral [2022/09/12 21:33] (current) 207.34.115.128 |
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<cite>The Lazy Universe by Coopersmith</cite></blockquote> | <cite>The Lazy Universe by Coopersmith</cite></blockquote> | ||
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- | * A perfect layman explanation of the path integral formalism can be found in the book Quantum Electrodynamics by Richard P. Feynman | ||
- | * See also: https://gravityandlevity.wordpress.com/2009/08/05/the-path-integral-calculating-the-future-from-an-unknown-past/ | ||
- | * http://www.thephysicsmill.com/2013/07/16/reality-is-the-feynman-path-integral/ | ||
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- | <tabbox Concrete> | ||
- | {{ :advanced_tools:feynmans_qed_probability_amplitudes.gif?nolink|}} | ||
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- | In the path integral formalism, we calculate the probability that a particle, which starts at some point $S$, ends up at some point $P$, by summing over all possible paths that connect $S$ and $P$. | ||
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- | For each path, we can calculate a probability amplitude $A_i$. To get the total probability that the particle ends up at $P$, we sum over all these amplitudes $A_i$ and then square the result. | ||
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- | Each amplitude is basically a [[basic_tools:complex_analysis|complex number]] and thus can be represented by an arrow in the complex plane. | ||
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<cite>Page 7 in QFT in a Nutshell by A. Zee</cite> | <cite>Page 7 in QFT in a Nutshell by A. Zee</cite> | ||
</blockquote> | </blockquote> | ||
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+ | |||
+ | |||
+ | ---- | ||
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+ | * A perfect layman explanation of the path integral formalism can be found in the book Quantum Electrodynamics by Richard P. Feynman | ||
+ | * See also: https://gravityandlevity.wordpress.com/2009/08/05/the-path-integral-calculating-the-future-from-an-unknown-past/ | ||
+ | * http://www.thephysicsmill.com/2013/07/16/reality-is-the-feynman-path-integral/ | ||
+ | |||
+ | | ||
+ | <tabbox Concrete> | ||
+ | {{ :advanced_tools:feynmans_qed_probability_amplitudes.gif?nolink|}} | ||
+ | |||
+ | In the path integral formalism, we calculate the probability that a particle, which starts at some point $S$, ends up at some point $P$, by summing over all possible paths that connect $S$ and $P$. | ||
+ | |||
+ | For each path, we can calculate a probability amplitude $A_i$. To get the total probability that the particle ends up at $P$, we sum over all these amplitudes $A_i$ and then square the result. | ||
+ | |||
+ | Each amplitude is basically a [[basic_tools:complex_analysis|complex number]] and thus can be represented by an arrow in the complex plane. | ||
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* Shankar, Principles of QM, the Chapter "Path integrals revisited" is especially useful for students interested in condensed matter physics. | * Shankar, Principles of QM, the Chapter "Path integrals revisited" is especially useful for students interested in condensed matter physics. | ||
* Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by H. Kleinert is the bible on path integrals. | * Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by H. Kleinert is the bible on path integrals. | ||
+ | * [[https://fondationlouisdebroglie.org/AFLB-312/aflb312m504.pdf|Majorana and the path-integral approach to | ||
+ | Quantum Mechanics]] by S. Esposito, Annales de la Fondation Louis de Broglie, Volume 31 no 2-3, pp. 207-225, 2006 | ||
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