theories:quantum_mechanics:canonical
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theories:quantum_mechanics:canonical [2018/05/11 16:01] jakobadmin |
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| - | In quantum mechanics, we no longer describe the trajectories of individual particles but only talk about probabilities that certain events can happen. | + | In quantum mechanics, we no longer describe the trajectories of individual particles but only talk about probabilities that certain events can happen. In the canonical description of quantum mechanics, we calculate these probabilities using a wave description for the particles. |
| - | So instead of describing the path between some points $A$ and $B$, we ask instead: "What's the probability that a particle which started at $A$ ends up at $B$?". | + | So instead of describing the path between some points $A$ and $B$, we ask instead: "What's the probability that a particle which started at $A$ ends up at $B$?". |
| + | Note that because particles are described by a wave, the points $A$ and $B$ will now correspond to points with highest probability of finding a particle there (being the highest point of the wave), as opposed to an exact point in space and time. | ||
| - | This idea is rooted in the observation that the only things that are actually important are those that we observe. Whatever happens between two measurements is not important, since we do not measure it. So when we do not measure the position of the particle between $A$ and $B$ it could have taken any path. | + | This idea of describing particles and their trajectories by waves is rooted in the observation that the only things that are actually important are those that we observe, the observation being any form of measurement. Whatever happens between two measurements is not important, since we do not measure it. So when we do not measure the position of the particle between $A$ and $B$ it could have taken any path. |
| While this sounds strange for everyday objects, this is the natural point of view for much tinier particles. We measure the position of a ball whenever we look at it. Such a measurement has no significant effect on the ball. | While this sounds strange for everyday objects, this is the natural point of view for much tinier particles. We measure the position of a ball whenever we look at it. Such a measurement has no significant effect on the ball. | ||
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| * Modern Quantum Mechanics by Jun John Sakurai | * Modern Quantum Mechanics by Jun John Sakurai | ||
| * The Principles of Quantum Mechanics by Paul Dirac | * The Principles of Quantum Mechanics by Paul Dirac | ||
| - | * Foundations of Quantum Mechanics by Gregory Naber for students who prefer a more mathematical treatment. | ||
| * Nice free lecture notes can be found [[https://www.colorado.edu/physics/phys7270/phys7270_fa16/lecnotes.html|here]]. | * Nice free lecture notes can be found [[https://www.colorado.edu/physics/phys7270/phys7270_fa16/lecnotes.html|here]]. | ||
| + | * See also [[https://www.isaacbooks.org/files/Ch1_qm2b.pdf|A Cavendish Quantum Mechanics Primer]] by M. Warner, FRS & A. C. H. Cheung which is a very gentle introduction aimed at highschool students. | ||
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| **The best abstract quantum mechanics textbooks are** | **The best abstract quantum mechanics textbooks are** | ||
| + | * Foundations of Quantum Mechanics by Gregory Naber for students who prefer a more mathematical treatment. | ||
| * Quantum Theory: Concepts and Methods by Asher Peres | * Quantum Theory: Concepts and Methods by Asher Peres | ||
| * Quantum Mechanics by L. E. Ballentine | * Quantum Mechanics by L. E. Ballentine | ||
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| ---- | ---- | ||
| - | The [[equations:canonical_commutation_relations|canonical commutation relations]] | + | The [[formulas:canonical_commutation_relations|canonical commutation relations]] |
| $$ [\hat{p},\hat{x}] = -i \hbar .$$ | $$ [\hat{p},\hat{x}] = -i \hbar .$$ | ||
theories/quantum_mechanics/canonical.1526047297.txt.gz · Last modified: 2018/05/11 14:01 (external edit)
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