Brus equation emission energy Δ"E" = "hc"/λ, where c is the speed of light). This is useful for calculating the radius of a quantum dot from experimentally determined parameters. The overall equation is "E", "m"*, and "m"* are unique for each nanocrystal composition. For example, with CdSe nanocrystals: Brus equation The Brus equation can be used to describe the emission energy of quantum dot semiconductor nanocrystals (such as CdSe nanocrystals) in terms of the band gap energy "E", Planck's constant "h", the radius of the quantum dot "r", as well as the effective mass of the excited electron "m"* and of the
Nonlinear Schrödinger equation Starting from the trivial solution "U" = 0 and iterating, one obtains the solutions with "n" solitons. The NLS equation is a partial differential equation like the Gross-Pitaevskii equation. Usually it does not have analytic solution and the same numerical methods used to solve the Gross-Pitaevskii equation, such as the split-step Crank–Nicolson and Fourier spectral methods, are used for its solution. There are different Fortran and C programs for its solution. The nonlinear Schrödinger equation is Galilean invariant in the following sense: Given a solution "ψ"("x, t") a new solution can be obtained by replacing "x" with "x" + "vt"