m (→Units) |
m (→Units) |
||
| (5 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
= Units = | = Units = | ||
| − | + | Units are a powerful tool. By combining quantities in SI units, you do not need to worry about conversion, as long as you know the dimension of the result. For instance, the [[Bohr radius]] formula is given by | |
| + | |||
| + | $$\displaystyle a_\mathrm{B}\equiv{4\pi\epsilon_0\hbar^2\over me^2}$$ | ||
| + | |||
| + | and has units of distance (it is a radius). We can work out its numerical value from the constants expressed in SI units without worrying about their conversion into the same set of units, e.g., that F=C$^2$/J: | ||
| + | |||
| + | <center><wz tip="The numerical value of the Bohr radius.">[[File:bohr-radius.png|500px]]</wz></center> | ||
| + | |||
| + | == Dimensionless units == | ||
| + | |||
| + | This being said, it is often convenient or elegant (or both) to dispose from the units, in which case space, time and energy all become the same thing. | ||
| + | |||
| + | This is elow a list of useful conversion factors between different units (they are handy to keep in mind): | ||
| + | |||
| + | === Time and energy === | ||
| + | |||
| + | Through the relation $E=\hbar\omega$, one gets (assuming $\hbar=1$) the following correspondence: | ||
$1~\mathrm{meV}=1.5193~\mathrm{ps}^{-1}$ | $1~\mathrm{meV}=1.5193~\mathrm{ps}^{-1}$ | ||
| − | Constants | + | == List of important fundamental Constants == |
$h\approx6.62607\times10^{-34}\mathrm{J s}$ | $h\approx6.62607\times10^{-34}\mathrm{J s}$ | ||
| + | |||
$h\approx4.13567\mathrm{\,meV\, ps}$ | $h\approx4.13567\mathrm{\,meV\, ps}$ | ||
| − | + | == Links == | |
| − | + | * [https://en.wikipedia.org/wiki/Natural_units Natural units] on the [[Wikipedia]]. | |
| − | + | ||
| − | + | ||
| − | + | ||
Latest revision as of 09:06, 1 May 2020
Contents |
Units
Units are a powerful tool. By combining quantities in SI units, you do not need to worry about conversion, as long as you know the dimension of the result. For instance, the Bohr radius formula is given by
$$\displaystyle a_\mathrm{B}\equiv{4\pi\epsilon_0\hbar^2\over me^2}$$
and has units of distance (it is a radius). We can work out its numerical value from the constants expressed in SI units without worrying about their conversion into the same set of units, e.g., that F=C$^2$/J:
Dimensionless units
This being said, it is often convenient or elegant (or both) to dispose from the units, in which case space, time and energy all become the same thing.
This is elow a list of useful conversion factors between different units (they are handy to keep in mind):
Time and energy
Through the relation $E=\hbar\omega$, one gets (assuming $\hbar=1$) the following correspondence:
$1~\mathrm{meV}=1.5193~\mathrm{ps}^{-1}$
List of important fundamental Constants
$h\approx6.62607\times10^{-34}\mathrm{J s}$
$h\approx4.13567\mathrm{\,meV\, ps}$
Links
- Natural units on the Wikipedia.