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## Homework Statement

hey im vaibhav,16 an 12th grade..just as pastime i tried to solve schrodinger equation in the 1D 2D 3D spaces. i got the 1D solution(not quantum oscillator), i seperated in 2D by polar coordinates but there is a problem in the radial equation

as for 3D i know that the solutions are such that i wont be doing em till im a wee bit older

but im just curious as the polar and radial eqautions are simply horrifying to contemplate solving

## Homework Equations

2D RADIAL EQUATION:

[tex]\hbar \frac{d}{dr} (\frac{rdR}{dr})+\frac{2m(Er+I)R}{\hbar}=[/tex][tex]\hbar[/tex]a

^{2}

where;

R"=second Derivative of R wrt r..similar for R'..R being radial wavefunction

r=radial distance from origin

I=intensity factor for a central force field ie of circular/spherical symmetry..(basically a constant explaining the field for a particular body)

## The Attempt at a Solution

after solving,normalizing(0,2\pi) i got the angular part of the 2D wavefunction as

Y

_{a}([tex]\theta[/tex])=[tex]\frac{exp(ia\theta)}{\sqrt{2\pi}}[/tex]

where "a" is quantized as any integer

exp(x)=e

^{x}

please see the attachments for the radial,polar equations in 2D;3D

also,

it would be helpful if anyone could suggest an easier way to get to the solutions of the radial, polar wavefunctions(im not that experienced..)..and also quantizing them..

thanks,

Vaibhav

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