Wave Nature of Electron

Confirmation of the DeBroglie hypothesis came in the Davisson- Germer experiment.

Examples of Electron Waves

Two specific examples supporting the wave nature of electrons as suggested in the DeBroglie hypothesis are the discrete atomic energy levels and the diffraction of electrons from crystal planes in solid materials. In the Bohr model of atomic energy levels, the electron waves can be visualized as "wrapping around" the circumference of an electron orbit in such a way as to experience constructive interference.

The wave nature of the electron must be invoked to explain the behavior of electrons when they are confined to dimensions on the order of the size of an atom. This wave nature is used for the quantum mechanical "particle in a box" and the result of this calculation is used to describe the density of energy states for electrons in solids.

DeBroglie Hypothesis

Another way of expressing this is 另一种表达方式是

Therefore, for a particle of zero rest mass 因此，对于一个静止质量为零的粒子 For a photon: 对于光子： The momentum-wavelength relationship for a photon can then be derived and this DeBroglie wavelength relationship applies to other particles as well. 光子的动量与波长关系可以推导出来，这种德布罗意波长关系也适用于其他粒子。

DeBroglie Wavelengths

The Davisson-Germer experiment showed that electrons exhibit the DeBroglie wavelength given by: 戴维森-格Mer实验表明，电子具有由下式给出的德布罗意波长：

If you explore the wavelength values for ordinary macroscopic objects like baseballs, you will find that their DeBroglie wavelengths are ridiculously small. Comparison of the power of ten for the wavelength will show that the wavelengths of ordinary objects are much smaller than a nucleus. The implication is that for ordinary objects, you will never see any evidence of their wave nature, and they can be considered to be particles for all practical purposes.

DeBroglie Wavelengths

The Davisson-Germer experiment showed that electrons exhibit the DeBroglie wavelength given by: 戴维森-格Mer实验表明，电子具有由下式给出的德布罗意波长：

For a particle of mass x10^ kg 对于质量为x10^ kg的质点 中文译文中的待填/计算数值依次对应：1：mb 2：mp。实际数值以上方原输入框为准。

=

=

traveling at velocity x10^ m/s
the associated DeBroglie wavelength is x10^m = m =nm.

You may enter values in any of the boxes. When you have finished entering data, click on the quantity you wish to calculate in the formula above. Wavelength values will be reconciled, but no further calculation will be done until you select which item you wish to calculate. Caution! This calculation is non-relativistic and accurate only for speeds much less than the speed of light. For speeds over a tenth of the speed of light a relativistic calculation should be used.

If you explore the wavelength values for ordinary macroscopic objects like baseballs, you will find that their DeBroglie wavelengths are ridiculously small. Comparison of the power of ten for the wavelength will show what the wavelengths of ordinary objects are much smaller than a nucleus. The implication is that for ordinary objects, you will never see any evidence of their wave nature, and they can be considered to be particles for all practical purposes. 如果你探索普通宏观物体如棒球的波长值，你会发现它们的德布罗意波长极其微小。比较波长的十次方幂可以显示普通物体的波长远小于原子核。其含义是，对于普通物体来说，你将永远无法观察到其波动性，因此可以认为它们在所有实际用途中都是粒子。