- #1
shinobi20
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Homework Statement
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.
Show that a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ
a and a† are the lowering and raising operators of quantum mechanics.
Homework Equations
3. The Attempt at a Solution [/B]Sorry but I really don't have any idea on how start. I just know that a=(1/ (2)½) (x/x0-ip/p0) and a†=(1/ (2)½) (x/x0+ip/p0) with x0=(ħ/mω)½ and p0=(ħmω)½