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
Frobenius solution to the hypergeometric equation get Now, Hence, Hence, At "c" = α we get "y". Hence, "y" = "E"′"y" + "F"′"y". Let "E"′"b" = "E" and "F"′"b" = "F". Noting that "s" = "x" we get From the symmetry of the situation here, we see that Frobenius solution to the hypergeometric equation In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series. This is usually the method we