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Dynamics of quantum systems, controlled by external fields

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Numerics.AtomicUnits

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All WavePacket codes are using atomic units throughout. These units are adapted to the classical Bohr model of the hydrogen atom in its ground state, see also the corresponding article in Wikipedia

Fundamental atomic units

In atomic units, Planck's (reduced) constant, electron rest mass, elementary charge, and the Coulomb constant are normalized to unity, see the following table

quantity	name	symbol	value
mass	electron rest mass	m_e	9.109 382 15(45) E-31 kg
electric charge	elementary charge	e	1.602 176 6208(98) E-19 C
angular momentum	Planck's constant	ℏ = h/(2π)	1.054 571 800(13) E-34 Js
electric constant	Coulomb constant	k_e = 1/(4πε₀)	8.987 551 787 3682 E9 kg·m³·s^-2·C^-2

where ε₀ = 8.854 187 817 E−12 As/(Vm) is the electric permittivity of vacuum.
Note that the atomic unit of mass (m_e) should not be confused with the '''atomic mass unit''' (or Dalton) 1u = 1g/mol = 1/12 m_12C = 1822.88839 m_e frequently used in atomic/molecular physics and in chemistry.

Derived atomic units

The above definition of fundamental units allows to derive the atomic units for all other quantities used in the WavePacket software, see the following table

quantity	definition	value
length (Bohr unit)	$a_0=\frac{4\pi\epsilon_0\hbar^2}{m_ee^2}=\frac{\hbar}{m_e \alpha c}$	52.917721 pm
energy (Hartree unit)	$E_h=\frac{m_e e^4}{(4\pi\epsilon_0\hbar)^2}=\alpha^2 m_e c^2$	4.359744 aJ
energy (electric potential)	E_h/e	27.211384 eV
energy (per amount of material)	E_hN_A	2625499.4 J/mol
energy (per amount of material)	E_hN_A	627509.4 cal/mol
force	E_h/a₀	82.387234983 nN
temperature	E_h/k_B	315774.6 K
wavenumber	1/λ = E_h/(hc) = ω/(2πc)	21947463 1/m
time	ℏ/E_h	24.188843 as
frequency	ν = E_h/ h	6.5796839 PHz
angular frequency	ω = E_h/ ℏ	41.341373 PHz
dipole moment	μ = ea₀	8.4783531 aC pm [ =2.541 746 D ]
electric field: F	E_h/(ea₀)	514.22064 GV/m
light intensity: cε₀F²/2	(E_h/(ea₀))²/(8πα)	35.094 PW/cm²

where the following constants have been used

c = 299792458 m/s is the vacuum speed of light
k_B = 1.380 648 52(79) E-23 J/K is Boltzmann's constant
N_A = 6.022 140 857(74) E23 1/mol is Avogadro's number
α = e²/(4πε₀ℏc) = 7.297 352 5664(17) E-3 = 1/137.035 999 139(31) is the fine structure constant (dimensionless)
Dipole moments are sometimes given in units of 1 Debye ≡ 1E-21 Cm / c = 3.33564 aC pm
Energies are sometimes given in units of 1 cal ≡ 4.184 J