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The Atomic System of Units
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Description
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By taking combinations of these four units, one can derive four units corresponding to the base dimensions length, mass, time, and electric current.
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To facilitate using atomic units, enter the command Units[UseContext](Atomic) so that the second, volt, and tesla refer to the atomic and not SI context.
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When used in conjunction with the UseSystem command, the atomic system sets the following units for the given dimensions. All units have context Atomic.
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Dimension Name
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Unit Name
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mass
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electron_mass
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electric charge
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electron
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action
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planck
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electric permittivity
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permittivity
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length
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bohr
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time
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second
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force
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hartree/bohr
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energy
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hartree
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power
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hartree per second
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electric current
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electron per second
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electric potential
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volt
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electric capacitance
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square electron per hartree
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electric field strength
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volt per bohr
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electric displacement
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electron per bohr squared
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electric dipole moment
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electron bohr
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electric polarizability
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electron bohr squared per volt
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magnetic permeability
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electron_mass bohr per electron squared
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magnetic flux
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volt second
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magnetic flux density
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tesla
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magnetic inductance
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volt second squared per electron
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magnetizing force
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hartree per tesla bohr cubed
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electric dipole moment
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hartree per tesla
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magnetic polarizability
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hartree per tesla squared
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Atomic Base Units
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All atomic base units have the context Atomic, including the second, where one atomic second is approximately  SI second.
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Dimension Name
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Unit Name
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Unit Symbol
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length
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bohr
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a0
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mass
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electron_mass
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em
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time
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second
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s
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electric current
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electron/second
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e/s
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Atomic Derived Units with Special Names and Symbols
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All units have the context Atomic.
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Dimension Name
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Unit Name
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Symbol
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In Terms of Other Atomic Units
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action
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planck
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h_bar +
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em*a0^2/s
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energy
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hartree
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E0
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em*a0^2/s^2
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electric permittivity
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permittivity
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kappa0
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s^2*e^2/a0^3/em
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electric potential difference
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volt
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V
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E0/e
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magnetic flux density
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tesla
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T
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em/s/e
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A plus sign (+) indicates an abbreviation.
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Examples
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| (1) |
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![convert(1.0, 'units', 'second[Atomic]', 's')](/support/helpjp/helpview.aspx?si=9447/file03259/math430.png)
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| (2) |
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| (3) |
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![convert(1.0, 'units', 'volt[Atomic]', 'V')](/support/helpjp/helpview.aspx?si=9447/file03259/math444.png)
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If infolevel is set to a greater integer (possible settings are 1 through 5), more detailed information about the computation method is displayed.
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![infolevel[Units] := 1](/support/helpjp/helpview.aspx?si=9447/file03259/math455.png)
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convert/system: "converting to the units e/a0^2"
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convert/system: "converting to the units e^2/E0"
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| (6) |
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![with(Units[Standard])](/support/helpjp/helpview.aspx?si=9447/file03259/math479.png)
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](/support/helpjp/helpview.aspx?si=9447/file03259/math483.png)
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](/support/helpjp/helpview.aspx?si=9447/file03259/math487.png)
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![2.532*Unit(a0/s[contexts:-Atomic])](/support/helpjp/helpview.aspx?si=9447/file03259/math494.png)
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![2.532*Unit('a0'/'s[SI]')](/support/helpjp/helpview.aspx?si=9447/file03259/math498.png)
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![0.1899015160e-14*Unit(a0/s[contexts:-Atomic])/Pi^3](/support/helpjp/helpview.aspx?si=9447/file03259/math501.png)
| (8) |
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![evalf(0.1899015160e-14*Unit(a0/s[second:-contexts:-Atomic])/Pi^3)](/support/helpjp/helpview.aspx?si=9447/file03259/math505.png)
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![0.6124615280e-16*Unit(a0/s[contexts:-Atomic])](/support/helpjp/helpview.aspx?si=9447/file03259/math508.png)
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| (10) |
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| (11) |
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![5*Unit(em/s[contexts:-Atomic]^2)](/support/helpjp/helpview.aspx?si=9447/file03259/math529.png)
| (12) |
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| (13) |
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| (14) |
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