Simple differential equation question

[n0_3sc]

If I have:
$$\frac{dA(t,z)}{dz}$$

is it possible to convert this to a differential in the form:
$$\frac{dI(t,z)}{dz}$$
given that $$I(t,z)=|A(t,z)|^2/a$$? (Where $$a$$ is a constant).

Any advice would help, thanks.

 

[tiny-tim]

hi n0_3sc!

dI(t,z)/dz would be (2/a) A(t,z).dA(t,z)/dz

 

[n0_3sc]

so there's no complex conjugate anywhere?

 

[tiny-tim]

now I'm totally confused

are you saying that A is complex, but I is real?

(and in any case, I has two copies of A, and A (obviously) only has one)

 

[n0_3sc]

Sorry, A is a complex quantity so |A(t,z)|^2=A(t,z)A*(t,z)

I'm confused about differentiating that.

 

[tiny-tim]

product rule … A'A* + AA'*

 

[n0_3sc]

thanks :)