If it makes you feel better, for every length $l$, define $l'=l/a_0$, and work only with $l'$.

yeah, you are not setting units to one, you are just absorbing them into your variables

I was kidding

Does anyone know how to do a Large Quotient

like this

yeah, you integrate in the complex $\hbar$ plane

Sorry, I can only do Medium Quotients

@ACuriousMind How?

@ACuriousMind A wild $\mathrm d_x^2 e^{-\beta |x|}$ appeared. What do?

$\delta(x)$ potential

use $e^{-|x|}=e^x\Theta(-x)+e^{-x}\Theta(x)$

and $\Theta'(x)=\delta(x)$

That's atrocious

What is $\delta'(x)$

or, use the Sch. eq. to relate the second derivative of $\psi$ with $V(x)\psi(x)$

I'm doing a variational problem so I don't know the energy

why

why what?

why tho

WHY WHAT THO

I think I'm supposed to use that $\psi\approx \psi(0)$ near $0$

what

no

do as I said before

$\Theta'(x)=\delta(x()$

fuck it im not fixing it

So $$\int_\Bbb R \psi \psi'' =\int_{-\infty}^0 \psi \psi''+\int_0^\infty \psi \psi''+\psi(0)\lim_{\epsilon\searrow 0}[\psi'(\epsilon)-\psi'(-\epsilon)] $$

use $$

Why

ok I got the energy as $\hbar \omega/\sqrt 2$

pretty close

pretty close to what? you should be able to find the exact result

your test function is actually the ground state

lol

ground state is a Gaussian

you lied to me

hmm?

you told me that the potential was $\delta(x)$

Where did I say that?

It's a Harmonic oscillator

why tho

Why what????

What why?

tho y

He's going to get taken out with an attitude like that

Lol, I'm el stupido

I thought that the square of a triangle was a triangle

Britain at it's finest

Howdy

sup

Nothing, you?

mathematica is great but fuck it is slow

You need patience for things like that

Like JavaScript, or Photoshop

ive been told that the code of photoshop is a true mess

and it gets messier with time

I wouldn't know

That sounds horrifying

I never like to imagine the code of huge applications

@BernardoMeurer youtube.com/watch?v=wAst3BYRVvA

@JohnRennie Check the link I posted up there

kbye peeps