Here, \ hbar is the reduced Planck constant, \ nabla is the nabla operator, \ mu is the reduced mass,-| e | ( + | e | ) is the elementary charge related to an electron ( hole ), \ varepsilon _ r is the relative permittivity, and \ varepsilon _ 0 is the vacuum permittivity.
42.
In a solid, the scaling of E _ \ lambda and the wavefunction size are orders of magnitude different from the hydrogen problem because the relative permittivity \ varepsilon _ r is roughly ten and the reduced mass in a solid is much smaller than the electron rest mass m _ e, i . e ., \ mu \ ll m _ e.
43.
The "'plane wave expansion "'method can be used to calculate the band structure using an DBR ) with air-core interleaved with a dielectric material of relative permittivity 12.25, and a lattice period to air-core thickness ratio ( d / a ) of 0.8, is solved using 101 planewaves over the first irreducible Brillouin zone.
44.
Where M _ 1 and M _ 2 are the charges per length in Coulomb meters, \ alpha _ 1 and \ alpha _ 2 are polarizability in units of C�m 2 �V " 1, { \ varepsilon _ 0 } represents the vacuum permittivity constant which is 8.85 . . . x 10 " 12 farads per meter, { \ varepsilon _ r } represents the relative permittivity of the surrounding material in farads per meter, \ mathrm { k } _ b is Boltzmann's Constant, T is Temperature in units of Kelvin, r is the distance between the molecules in meters, and the hV terms refer to the ionization energies of the molecules.
