/sci/ - Science & Math

>Any job I want.
>$inf starting

Don't mind me, I'm just solving the hydrogen atom
<div class="math">\Psi_{nlm}(r,\vartheta,\varphi) = \sqrt {{\left(\frac{2}{n a_0}\right)}^3\frac{(n-\ell-1)!}{2n((n+\ell)!)} } e^{- \frac{r}{n a_0}} \left(\frac{2r}{n a_0}\right)^\ell \frac{e^\frac{2r}{n a_0} \left(\frac{2r}{n a_0}\right)^{-{(2\ell+1)}}}{(n-\ell-1)!} \frac{{\rm d}^{n-\ell-1}}{{\rm d}\left(\frac{2r}{n a_0}\right)^{n-\ell-1}} \left(e^{-\frac{2r}{n a_0}}\left(\frac{2r}{n a_0}\right)^{l+n}\right) \cdot \, \frac{1}{\sqrt{2\pi}} \sqrt{\frac{2 \ell +1}{2}\cdot\frac{(\ell -m)!}{(\ell +m)!}}\,\, \frac{(-1)^m}{2^\ell \, \ell!} \left(1-(\cos\vartheta)^2\right)^\frac{m}{2} \frac{\mathrm{d}^{\ell+m}}{\mathrm{d}(\cos\vartheta)^{\ell+m}} \left(\left((\cos\vartheta)^2-1\right)^\ell\right) e^{im\varphi}</div>

>>1215731
Cool copypasta, bro.

>>1215731
DAT MATH

>>1215746
I wrote that down myself, and yes, it was a very annoying process.

>>1215751
Seems like you could have made more of an effort to simplify, bro.

>>1215766

>>1215764
Feel free to contribute, I'm not touching that TeX file ever again.

>>1215772
Well, the first thing that bugs me is the numerous instances of (2r/(na.)). I assume a. and n are constants. Factor out the r and collect all instances of (2/(na.)) and toss them all in with those lonely 3 under that first radical.
Or even substitute (2r/(na.)) for some other variable. I notice you differentiate with respect to that mess a few times. Why, nigga?

>>1215803
The original formulas involve expressions such as <span class="math">\varrho = \frac{2r}{na_0}[/spoiler]. I wanted to get it all into one equation, so I had to insert the abbreviation in full length.

>>1215772
Take a few tips from mine. Look how short and neat it is.

>>1215811
The original formulas had the right idea.

>>1215815
Naah. Like this you can still see what the radial/angular parts are, mashing the normalizations together will just result in a mess maths and physics wise.

>>1215828
Making that substitution would still allow you to write it as a product of three functions: one in terms of r (or 2r/(na)), one in terms of theta, and one in terms of phi. This is what I assume you mean by separating the radial parts from the rest.

Jw: Did you arrive at this solution in a similar way to deriving the plane-wave solution to the general wave equation? (ie: products of functions of each variable)

just a test:
<span class="math">\int \frac{\mathrm{d} x}{x^n + a^n}=\frac{-1}{n a^{n-1}}\sum_{k=0}^{n-1}\left [ \frac{ln(x-a e^{i \frac{\pi}{n}(1+2k)})}{e^{i \frac{\pi}{n}(1+2k)}} \right ] + C[/spoiler]

>>1215828
So I just googled "Hydrogen wave function."
http://en.wikipedia.org/wiki/Hydrogen_atom#Wavefunction
It really is a solution in terms of products of individual functions.
It is far easier to look at and think about written in its component parts rather than all together. AND they make the substitution I suggest and you informed me about (rho=2r/an). I was trolling before, but seriously: Why would you write it like that?

I need to take a higher physics course. :[ this stuff is interesting looking.

YOU STILL HERE JOSEF?
I'm interested in your response to these two posts:
>>1215871
>>1215948

>>1215688
is the op's equation right?! ive never been able to integrate above n=2

>>1215987
Take a derivative and combine all the fractions. See for yourself.

>>1215900


might looks better like this

<div class="math">\int \frac{\mathrm{d} x}{x^n + a^n}=\frac{-1}{n a^{n-1}}\sum_{k=0}^{n-1}\left [ \frac{ln(x-a e^{i \frac{\pi}{n}(1+2k)})}{e^{i \frac{\pi}{n}(1+2k)}} \right ] + C</div>

>>1216008
How did you do that?

>>1216014

miracles

no really, just replace math by eqn

wwｗ._ａｎｏＮ_+_Ｍ_-_ｍ_+_TＡＬK_.sＥ jcg wwho j sk do zbabd zwu f uifvk vz kzcitfiz i

>>1216016
eqn's how do they work?
<div class="math">\int \int \int \int \int \int \int \int \int wut</div>

>>1215731

Joseph, what does the function <div class="math">\Psi_{nlm}(r,\vartheta,\varphi)</div> actually express?

>>1216016
I LOVE YOU

>>1216036
http://en.wikipedia.org/wiki/Hydrogen_atom#Wavefunction

And these are my realization to what's going on.
>>1215871
>>1215948

>>1216016

Testing:

<div class="math"> \Gamma(z)=\int_{0}^{\infty }t^{z-1}e^{-t}dt </div>