User:DJIndica/Sandbox

Inglis-Teller limit

The linear Stark shift is given by

$\Delta E_{\text{S}}={\frac {3}{2}}er_{n}F,$

where e is the elementary charge, radius of the n^th electron orbit in the Bohr model of the hydrogen atom and F is the component of the local electric field parallel with the electric dipole. The energy of the n^th electron orbit is simply the Coulomb potential energy with r = r_n

$U_{n}=-{\dfrac {1}{4\pi \varepsilon _{0}}}{\dfrac {e^{2}}{r_{n}}}=-\left({\dfrac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}{\dfrac {m_{e}}{n^{2}}},$

giving an energy level spacing

$\Delta U_{n}=\left({\dfrac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}{\dfrac {2m_{e}}{n^{2}}}.$

The Inglis-Teller limit is defined as the field strength at which the Stark states with |(n₁ - n₂)| = n are shifted by half of this spacing, ΔE_S = ΔU_n/2,

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \rightarrow F = }