# Who introduced the Green function method into quantum mechanics?

Its power is amazing. For a Hamiltonian, you define the Green function as

$$G = \frac{1}{\lambda E-H} .$$

Who first come up with this definition? What was the motivation?

• Probably someone named Green – tox123 Mar 27 '16 at 20:19

This is not quite the definition of the Green function, but rather of the resolvent, more traditional notation is $R_{\lambda}:=(\lambda E-H)^{-1}$ with $H$ the Hamiltonian of the system and $E$ the identity operator. When $H$ is a differential operator, as the Schrodinger operator with some boundary conditions for example, this resolvent can be represented by an integral operator, whose kernel is called the Green function, i.e. $(R_{\lambda}f)(x)=\int G_{\lambda}(x,y)f(y)\,dy$. The resolvent formalism for integral operators was originally developed by Fredholm in 1903, the name is due to Hilbert.