- #1
Bazman
- 21
- 0
Hi,
I'm having trouble following the following derivation I have seen in a textbook:
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?
I'm having trouble following the following derivation I have seen in a textbook:
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?