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I'm having trouble following the following derivation I have seen in a text book:

The derivation goes as follows:

L0P3+L1P2+L2P1=0

This is a Poisson eqn for P3 with respect to L0 which requires

<L1P2+L2P1>=0

<L2>=L(BS)(sigma)

<L1P2>=.5<L1.phi(y)>.x^2. d^2P0/dx^2

thus

L(BS)(sigma).P1=.5<L1.phi(y)>.x^2. d^2P0/dx^2 eq 1

<L1.phi(y).>=sqrt(2).p.v.<f(y).phi`(y)>.x. d/dx - sqrt(2).v<A(y)phi`(y)>. eq 2

now according to the derivation when you substitute eq 2 into 1 you get:

<L1.phi(y).>=sqrt(2)/2.p.v.<f(y).phi`(y)>.x^3. d^3/dx^3 +(sqrt(2).p.v.<f

(y).phi`(y)> - sqrt(2)/2.v<A(y)phi`(y)>).x^2. d^2/dx^2 eq 3

now it seems from the above that the x in:

x. d/dx . x^2.d^2P0/dx^2

is treated like a constant while the product rule is just applied to the d/dx . x^2.d^2P0/dx^2 part.

Is this correct? If so can someone please explain why the x^2 and the x term are not grouped together?

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