Partial differentiation

[fickle hamlet]

How does this happen

[karmic mulch]

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[fickle hamlet]

by the way this was while I was deriving the expression for schrodinger's equation in spherical coordinate system

[unkempt phoenix]

umm

you just differentiate r^2 twice

[fickle hamlet]

uhmmm

okay let me try

that is

0

no

1

no

2

yeah

[unkempt phoenix]

the notation is not consistent either

[fickle hamlet]

then ?

[unkempt phoenix]

what does this mean for instance?

[fickle hamlet]

this is just the operator

the partial derivative operator

i have the equation screenshot

[unkempt phoenix]

applied to r^2?

[fickle hamlet]

how do i send it

[unkempt phoenix]

im asking because how is one supposed to read this

[fickle hamlet]

yeah i have the correct screenshot

where do i share

[unkempt phoenix]

post it here

drag n drop

[fickle hamlet]

oh okay

here

[unkempt phoenix]

so this part

with out the - ... at the end

[fickle hamlet]

yes

[unkempt phoenix]

find out how you're supposed to read this expression

does the operator apply to what is before it, or after it

[fickle hamlet]

okay

so i dont think its applying on r

its defnitely not being applied on r

[unkempt phoenix]

$$ \frac{1}{r} \frac{\partial^2}{\partial r^2} = \frac{2}{r^3} $$

then?

[vocal fog]

aL

[unkempt phoenix]

so let's suppose it's like that

then on the LHS

[fickle hamlet]

okay

[unkempt phoenix]

$$ \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial}{\partial r} \right) = -\frac{2}{r^3}r^2 \frac{\partial}{\partial r} $$

[vocal fog]

aL

[fickle hamlet]

omg

wait lemme read

[fickle hamlet]

but howcome did this result show up

since its just an operator

its not being applied on anything

[unkempt phoenix]

$$= -\frac{2}{r}\frac{\partial}{\partial r} = \frac{2}{r^2}$$

[vocal fog]

aL

[unkempt phoenix]

and you have the same thing on the RHS

[fickle hamlet]

let me check

[unkempt phoenix]

the operator applies to what is on the left

[fickle hamlet]

whatt

really ???

[unkempt phoenix]

yes, physicist notation

$$ \frac{1}{r} \frac{\partial^2}{\partial r^2}r = \frac{2}{r^3}r = \frac{2}{r^2} $$

[vocal fog]

aL

[fickle hamlet]

so that is what is happening in the above equation ?

[unkempt phoenix]

beats me, not my field of study

[fickle hamlet]

i dont think so

because i didnt study operator applying to its left

[unkempt phoenix]

well in this case it does

[fickle hamlet]

thats weird

[unkempt phoenix]

.

[fickle hamlet]

since this is my first time

coming across something like this

[unkempt phoenix]

it's not unusual

in math sometimes it's also written xf instead of f(x)

old school writing style

[unkempt phoenix]

well you have to because there is nothing to the right from the operator here

[fickle hamlet]

okay wait let me check

okay that is because

its just an operator

[unkempt phoenix]

this is only way the equality makes sense

[fickle hamlet]

its not a complete equation

maybe if we apply a function after the nebla

[unkempt phoenix]

it's a decomposition of the laplacian

as said in the text

[fickle hamlet]

yes

[unkempt phoenix]

these equalities are true

[fickle hamlet]

yeah the first one i know

maybe if we apply a function after the laplacian

[unkempt phoenix]

well, it's your study material, read it and it will hopefully make sense

and if it's a physics textbook, ..pray

[fickle hamlet]

it is

Quantum Mechanics textbook

gg

professor is weird, he said he explained it in the classs, and wont say anything more

[unkempt phoenix]

why is that weird

[fickle hamlet]

because i wasn't present .__.

and he knows that

[unkempt phoenix]

good professor, not giving special treatment

[fickle hamlet]

lmaoaoa

okay let me try

to come up with something

ill let you know

here

[unkempt phoenix]

it's just a small calculation to verify the equality in question

[fickle hamlet]

yes

OKAY

figuredd outt !!!

let me send u the pic wait

@unkempt phoenix look

both give the same result

and psi is some function of r

i just applied psi on rhs one

[unkempt phoenix]

could be, I don't know the rules of reading this text

[fickle hamlet]

.___.

basically psi is some function and we are applying the operators on it

anyway

thankyou sm

+close