# 玻恩定則

## 概述

### 離散值譜

${\displaystyle O_{i}}$ ${\displaystyle |O_{i}\rangle }$ ${\displaystyle i=1,\ 2,\ 3,\ \cdots ,n}$

${\displaystyle p(O_{i})=|\langle O_{i}|\psi \rangle |^{2}}$

### 連續值譜

${\displaystyle x}$ ${\displaystyle |x\rangle }$ ${\displaystyle -\infty \leq x\leq \infty }$

${\displaystyle p(a\leq x\leq b)=\int _{a}^{b}|\langle x|\psi \rangle |^{2}\mathrm {d} x}$

## 參考文獻

1. ^ Zurek, Wojciech. Quantum Darwinism, Classical Reality, and the randomness of quantum jumps. Physics Today. 2014, 67 (10): 44–45.
2. ^ Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë. Quantum Mechanics Volume 1. Hermann. ISBN 978-2-7056-8392-4.
3. Schlosshauer, Maximilian; Fine, Arthur. On Zurek’s Derivation of the Born Rule (PDF). Foundations of Physics. 2005, 35 (2): 197–213. doi:10.1007/s10701-004-1941-6.
4. ^ Landsman, Nicolaas, Born Rule and its Interpretation (PDF), (编) Greenberger, Daniel; 等, Compendium of Quantum Physics, Springer: 64–70, 2009, ISBN 978-3-540-70622-9, doi:10.1007/978-3-540-70626-7_20, The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle. 缺少或|title=为空 (帮助)
5. Griffiths, David J., Introduction to Quantum Mechanics (2nd ed.), Prentice Hall, 2004, ISBN 0-13-111892-7
6. ^ Zur Quantenmechanik der Stoßvorgänge, Max Born, Zeitschrift für Physik, 37, #12 (Dec. 1926), pp. 863–867 (German); English translation, On the quantum mechanics of collisions, in Quantum theory and measurement, section I.2, J. A. Wheeler and W. H. Zurek, eds., Princeton, New Jersey: Princeton University Press, 1983, ISBN 0-691-08316-9.
7. ^ Born, Max. Born's Nobel Lecture on the statistical interpretation of quantum mechanics (PDF). Nobel Lecture. NobelPrize.org. 1954. Again an idea of Einstein’s gave me the lead. He had tried to make the duality of particles - light quanta or photons - and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons.
8. ^ The Nobel Prize in Physics 1954. NobelPrize.org. 1954.
9. ^ Mathematische Grundlagen der Quantenmechanik, John von Neumann, Berlin: Springer, 1932 (German); English translation Mathematical Foundations of Quantum Mechanics, transl. Robert T. Beyer, Princeton, New Jersey: Princeton University Press, 1955.