On the operator equation AX-XB=C

This work studies how certain problems in quantum theory have motivated some recent research in pure Mathematics in matrix and operator theory. The mathematical key is that of a commutator or a generalized commutator, that is, find an operator $X\in B(H)$ satisfying the operator equation $AX-XB=C$. By this we will show how and why to solve the operator equation $AX-XB=C$. As application we recall the solurion of $AXB-CXD=E$ and we use the solution of this equation to solve equation of Monkeypox Diseases.