Difference between revisions of "Quantum Mechanics"
KevinYager (talk | contribs) (Created page with "==Postulates== ===Postulate 1=== A quantum system is completely specified by its '''Wave Function'''. :<math> \psi(x) </math> ==See Also== * [http://en.wikipedia.org/wiki/Qu...") |
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==Postulates== | ==Postulates== | ||
| − | === | + | ===Wavefunction=== |
| − | A quantum system is completely specified by its '''Wave Function''' | + | A quantum system is completely specified by its '''Wave Function''': |
:<math> | :<math> | ||
\psi(x) | \psi(x) | ||
</math> | </math> | ||
| + | The wavefunction is typically normalized: | ||
| + | |||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | ! Integral Notation | ||
| + | ! Dirac Notation | ||
| + | |- | ||
| + | | <math>\int | \psi(x) |^2 \mathrm{d}x = 1</math> | ||
| + | | <math> \langle \psi | \psi \rangle = 1</math> | ||
| + | |} | ||
| + | |||
| + | The distribution of the particle described by <math>\psi(x)</math> is given by: | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | ! Integral Notation | ||
| + | ! Dirac Notation | ||
| + | |- | ||
| + | | <math> \Pr(x) \mathrm{d}x = | \psi(x) |^2 </math> | ||
| + | | <math> |\langle x | \psi \rangle |^2 </math> | ||
| + | |} | ||
| + | |||
| + | In the Copenhagen Interpretation, <math>\Pr(x)</math> is the probability of finding the particle at location <math>x</math>. In Universal Wave Function interpretations (e.g. MWI), <math>\Pr(x)</math> can be thought of as the spatial distribution of the particle. | ||
==See Also== | ==See Also== | ||
* [http://en.wikipedia.org/wiki/Quantum_mechanics Wikipedia: Quantum Mechanics] | * [http://en.wikipedia.org/wiki/Quantum_mechanics Wikipedia: Quantum Mechanics] | ||
Revision as of 15:00, 12 October 2014
Postulates
Wavefunction
A quantum system is completely specified by its Wave Function:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \psi(x) }
The wavefunction is typically normalized:
| Integral Notation | Dirac Notation |
|---|---|
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int | \psi(x) |^2 \mathrm{d}x = 1} | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \langle \psi | \psi \rangle = 1} |
The distribution of the particle described by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \psi(x)} is given by:
| Integral Notation | Dirac Notation |
|---|---|
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Pr(x) \mathrm{d}x = | \psi(x) |^2 } | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\langle x | \psi \rangle |^2 } |
In the Copenhagen Interpretation, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Pr(x)} is the probability of finding the particle at location Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} . In Universal Wave Function interpretations (e.g. MWI), Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Pr(x)} can be thought of as the spatial distribution of the particle.
