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
Matrix difference equation meaning that "H" converges to a particular fixed matrix "H"* which may be irrational even if all the other matrices are rational. See also Stochastic control#Discrete time. A related Riccati equation is in which the matrices "X", "A", "B", "C", and "E" are all "n"×"n". This equation can be solved explicitly. Suppose formula_37, which certainly holds for "t"=0 with "N" = "X" and with "D" equal to the identity matrix. Then using this in the difference equation yields so by induction the form formula_42 holds for all "t". Then the evolution of "N" and "D" can be written as Thus