DeBroglie Wavelength

德布罗意波长

A convenient form for the DeBroglie wavelength expression is

where hc = 1239.84 eV nm and pc is
expressed in electron volts.

其中 hc = 1239.84 eV nm，而 pc 以电子伏特为单位表示。

This is particularly appropriate for comparison with photon wavelengths since for the photon, pc=E and a 1 eV photon is seen immediately to have a wavelength of 1240 nm. For massive particles with kinetic energy KE which is much less than their rest mass energies:

这尤其适用于与光子波长进行比较，因为对于光子来说，pc=E，一个1 eV的光子立即可以看出来其波长为1240 nm。对于具有动能KE的宏观粒子，当其动能远小于其静止质量能量时：

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For an electron with KE = 1 eV and rest mass energy 0.511 MeV, the associated DeBroglie wavelength is 1.23 nm, about a thousand times smaller than a 1 eV photon. (This is why the limiting resolution of an electron microscope is much higher than that of an optical microscope.)

对于一个具有动能1 eV、静止质量能量0.511 MeV的电子，其对应的德布罗意波长为1.23 nm，大约是1 eV光子波长的千分之一。（这就是为什么电子显微镜的极限分辨率远高于光学显微镜。）

The following calculation uses the full relativistic expressions for kinetic energy, etc.

以下计算使用了完整的相对论表达式，如动能等

For rest mass m₀ = m_e =m_p=x10^kg

对于静止质量 m₀ = mₑ = mₚ = 10⁵ kg

中文译文中的待填/计算数值依次对应：1：me 2：mp 3：mb 4：mpp。实际数值以上方原输入框为准。

where m_e= electron rest mass and m_p= proton rest mass,

其中 m_e 是电子静止质量，m_p 是质子静止质量，

and kinetic energy KE = eV =MeV = GeV
= x10^joules

并有动能 KE = eV = MeV = GeV = x10^ 焦耳

中文译文中的待填/计算数值依次对应：1：ev 2：mev 3：gev 4：eb 5：ep。实际数值以上方原输入框为准。

corresponding to velocity v =x10^m/s = c,

对应速度为 v = x10^ m/s = c,

中文译文中的待填/计算数值依次对应：1：vb 2：vp 3：vc。实际数值以上方原输入框为准。

the corresponding DeBroglie wavelength is
λ = x10^m =nm =fermi.

相应的德布罗意波长是 λ = x10^ m = nm = 佛米。

中文译文中的待填/计算数值依次对应：1：dwb 2：dwp 3：dnm 4：dfm。实际数值以上方原输入框为准。

Caution! Since this calculation was designed for speeds which are a significant fraction of the speed of light, it may lose some accuracy for very low speeds. Under those conditions, small differences between large numbers occur in the calculations. For low speed calculations like the baseball example, it might be more accurate to use the non-relativistic calculation.

注意！由于该计算是为速度接近光速的情况设计的，因此在非常低的速度下可能会失去一些准确性。在这些条件下，大数之间的微小差异会在计算中出现。对于低速情况，如棒球的例子，可能更准确的是使用非相对论的计算方法。

Low velocity calculation of DeBroglie wavelength

低速德布罗意波长计算

德布罗意波长表达式的一个方便形式是

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Usefulness of the Quantity pc

量 pc 的实用性

The relativistic energy expression for a particle is:

质点的相对论能量表达式为：

which reduces to E = pc for photons . The quantity pc is proportional to the relativistic momentum but has energy units, and it is useful in many high energy calculations. Using

这简化为 E = pc 对于光子而言。量 pc 是与相对论动量成正比的，但具有能量的单位，并且在许多高能计算中很有用。使用

and

并且

an expression for pc in terms of the relativistic kinetic energy can be obtained:

一个用相对论动能表示 pc 的表达式可以得到：

Application to pion decay

应用于π介子衰变

For most ordinary processes the kinetic energy is much less than the rest mass energy, so the first term can usually be neglected. This leads to the useful approximation:

对于大多数普通过程，动能远小于静止质量能量，因此第一项通常可以忽略。这导致了有用的近似：

For electron energies less than 20 keV and proton energies less than 38 MeV this expression has an error less than 1%.

对于电子能量小于20 keV且质子能量小于38 MeV的情况，该表达式的误差小于1%。

For extreme relativistic velocities where

在极端相对论性速度的情况下，其中