1. The problem statement, all variables and given/known data Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L. Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½. with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length. a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ a and a† are the lowering and raising operators of quantum mechanics. Show that H=ħωc(a†a + ½) 2. Relevant equations L=ħc/eB, ωc=eB/mc (cyclotron frequency), e for the charge of the electron H = Px2/2m + ( Py2 + eBx/c )2/2m 3. The attempt at a solution I have tried to find x,y,∂x,∂y in terms of n,ñ,∂n,∂ñ. But I ended up getting only some if the right terms to come out but not all, is my first step wrong? Any suggestions?