By F. David Peat

ISBN-10: 0809245124

ISBN-13: 9780809245123

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**Extra resources for Complementarity and the Copenhagen Interpretation of Quantum Mechanics**

**Example text**

42) 9 When an electron–positron pair annihilate, they produce at least two photons each having an energy m c2 e 0511 MeV. 18 CHAPTER 1. ORIGINS OF QUANTUM PHYSICS If the photon’s energy is smaller than 102 MeV, no pair will be produced. 1 de Broglie’s Hypothesis: Matter Waves As discussed above—in the photoelectric effect, the Compton effect, and the pair production effect—radiation exhibits particle-like characteristics in addition to its wave nature. In 1923 de Broglie took things even further by suggesting that this wave–particle duality is not restricted to radiation, but must be universal: all material particles should also display a dual wave–particle behavior.

In 1916 Wilson and Sommerfeld offered a scheme that included both quantization rules as special cases. 7. QUANTIZATION RULES 37 where n is a quantum+number, p is the momentum conjugate associated with the coordinate q; the closed integral is taken over one period of q. This relation is known as the Wilson– Sommerfeld quantization rule. 86) leads to Planck’s quantization relation E nhF.

B) The radii of the three lowest states of the positronium are given by r1 2a0 0106 nm, r2 8a0 0424 nm, and r3 18a0 0954 nm. The corresponding energies are E 1 1 21 R 68 eV, E 2 81 R 17 eV, and E 3 18 R 0756 eV. 63) that Bohr postulated to account for the quantization of the electron’s orbital angular momentum, L n h . A number of attempts were undertaken to understand or interpret these rules. In 1916 Wilson and Sommerfeld offered a scheme that included both quantization rules as special cases.

### Complementarity and the Copenhagen Interpretation of Quantum Mechanics by F. David Peat

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