Quantum mechanics

Uncertainty principle

Introduction · Mathematical formulation Background Classical mechanics Old quantum theory Interference · Bra-ket notation Hamiltonian Fundamental concepts Quantum state · Wave function Superposition · Entanglement Measurement · Uncertainty Exclusion · Duality Decoherence · Ehrenfest theorem · Tunneling Experiments Double-slit experiment Davisson–Germer experiment Stern–Gerlach experiment Bell's inequality experiment Popper's experiment Schrödinger's cat Elitzur-Vaidman bomb-tester Quantum eraser Formulations Schrödinger picture Heisenberg picture Interaction picture Matrix mechanics Sum over histories Equations Schrödinger equation Pauli equation Klein–Gordon equation Dirac equation Bohr Theory and Balmer-Rydberg Equation Interpretations Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional Advanced topics Quantum information science scattering theory Quantum field theory Scientists Planck · Einstein · Bohr · Sommerfeld · Bose · Kramers · Heisenberg· Born · Jordan · Pauli · Dirac · de Broglie ·Schrödinger · von Neumann · Wigner · Feynman · Candlin · Bohm · Everett · Bell · Wien

This box: view • talk • edit

The Davisson–Germer experiment was a physics experiment conducted in 1927 which confirmed the de Broglie hypothesis, which says that particles of matter (such as electrons) have wave properties. This demonstration of wave-particle duality was important historically in the establishment of quantum mechanics and of the Schrödinger equation.

Contents 1 History 2 Experiment 3 See also 4 References 5 External links

[edit] History

In 1924 Louis de Broglie presented his thesis concerning the wave-particle, proposing the idea that all matter displayed the wave-particle duality of photons.^[1] According to de Broglie, for all matter and for radiation alike, the energy E of the particle was related to the frequency of its associated wave ν, by the Planck relation

and that the momentum of the particle p was related to its wavelength λ by what is now known as the de Broglie relation

where h is Planck's constant.

In 1926, upon knowing the preliminary results of Davisson and Germer, Walter Elsasser remarked that the wave-like nature of matter might be investigated by electron scattering experiments on crystalline solids, as the wave-like nature of X-rays was confirmed through X-ray scattering experiments on crystalline solids.^[1][2]

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline nickel target.^[3] The angular dependence of the reflected electron intensity was measured, and was determined to have the same diffraction pattern as those predicted by Bragg for X-rays. This was also replicated by George Paget Thomson.^[1]

The experiment confirmed the de Broglie hypothesis – matter displayed wave-like behaviour. This, in combination with Arthur Compton's experiment, established the wave particle duality hypothesis, which was a fundamental step in quantum theory.

[edit] Experiment

The experiment consisted of firing an electron beam from an electron gun on a nickel crystal at normal incidence (i.e. perpendicular to the surface of the crystal). The electron gun consisted of a heated filament that released thermally excited electrons, which were then accelerated through a potential difference V (giving them a kinetic energy of eV (e is the charge of an electron)). An electron detector was placed at an angle θ = 50° and measured the number of electrons that were scattered at that particular angle.^[1]

According to the de Broglie relation, a beam of 54 eV had a wavelength of 0.165 nm. This matched the predictions of Bragg's law

for n = 1, θ = 50°, and for the spacing of the crystalline planes of nickel (d = 0.091 nm) obtained from previous X-ray scattering experiments on crystalline nickel.^[1]

[edit] See also

• de Broglie wavelength

[edit] References

1. ^ ^{a b c d e} R. Eisberg, R. Resnick (1985). "Chapter 3 – de Broglie's Postulate—Wavelike Properties of Particles". Quantum Physics: of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). John Wiley & Sons. ISBN 0-471-87373-X. 
2. ^ H. Rubin. "Walter m. Elsasser". National Academies Press. http://www.nap.edu/openbook.php?record_id=4990&page=103. Retrieved 2008-08-26. 
3. ^ C.Davisson, L.H. Germer (1927). "Reflection of electrons by a crystal of nickel". Nature 119: 558–560. doi:10.1038/119558a0. 

[edit] External links

• Page at Hyperphysics project, Georgia State University