/sci/ - Science & Math

>>14866559
>>14866577
>>14866582
¯\_(ツ)_/¯

>>14854820
>>14854841
11 is an excellent number

https://satanslibrary.org/English/Torah_and_the_Jews_Exposed.pdf

https://satanisgod.org/www.angelfire.com/empire/serpentis666/HOME.html

>>14546197
>You just integrate componentwise, there's nothing nonsensical about it.
Then your post doesn't make sense.
[math]\displaystyle \langle \psi | \nabla | \psi \rangle +\langle \psi | \nabla| \psi \rangle^* = \lim_{R\to\infty}\oint_{|\vec x|=R} |\psi|^2 d\vec S[/math]
The term on the left is, according to you, a three-component vector (unless I'm misunderstanding what do you mean by integrating component-wise). But how do you integrate the term on the right component-wise to get a vector when it's a regular number-valued surface integral?
Further, I can construct a counterexample easily enough for [math]\psi: \mathbb{R} \to \mathbb{R}[/math]. Set [math]\phi (x) = 1/x \cos (x^4)[/math]. Define [math]\psi(x) = \phi (x)[/math] when [math]|x| \geq 1[/math] and stitch in some smooth bounded function for [math]|x| < 1[/math]. Then [math]\psi(x) \dfrac{d}{dx} \psi (x) = - \dfrac{1}{x} \cos (x^4) \dfrac{4x^4 \sin (x^4) + \cos(x^4)}{x^2}[/math], which isn't even integrable on [math]\mathbb{R}[/math].
>How else would you interpret [math]\langle \psi | \nabla | \psi \rangle[/math]?
I think he just posted it incorrectly and meant [math]\langle \psi | \Delta | \psi \rangle[/math].
Which, mind you, doesn't actually work under the conditions he posted, but it does work if you assume [math]\psi[/math] is in the Schwartz space, which physicists usually do willy nilly.