# Wave Function

## Homework Statement

One wave function of H like atom is $$\psi=\frac{\sqrt{2}}{81\sqrt{\pi}a_{0}^{3/2}}(6-\frac{r}{a_{0}})\frac{r}{a_{0}}(e^{\frac{-r}{3a_{0}}})cos \theta$$

How many nodal surfaces are there?
1)1
2)2
3)3
4)none of these

## The Attempt at a Solution

Its an objective question which I need to answer in less than a minute. Is it possible to do so?

The next thing that I assume i that the wave function is given in polar coordinate form, isn't it?? $$\psi=f(r,\theta, \phi)$$???
phi is absent what does it mean? I guess it means that its the p - orbital. then the anwer must be 2. Am I right????

Last but not the least. I am keen upon seeing the 3D picture this wave function generates. I have MATLAB but I dont know how to code in polar coordinate and all. Will somebody code this wave function for me which is compatible with MATLAB 2008?? Please. I shall be very grateful.
Thanks a lot.

## Answers and Replies

Isn't the number of nodal surfaces equal to the quantum number of your wave function?

Isn't the number of nodal surfaces equal to the quantum number of your wave function?

Thanks a lot but I know that already. Is it of any help with this particular problem?
And sir, can you please tell me how can I plot equations such as this one and like
x2+y2+z2=1 with MATLAB?

Your given the wave function. The wave functions for the hydrogen atom are constructed from two separate functions, the spherical harmonic wave functions, $$Y^{m}_{l}\left(\theta,\phi\right)$$, and the radial wave functions, $$R_{nl}\left(r\right)$$:

$$\Psi_{nlm}\left(r,\theta,\phi\right) = R_{nl}\left(r\right)Y^{m}_{l}\left(\theta,\phi\right)$$

You really only need to look at the radial wave equation, since by definition it has a term $$e^{-r/na}$$, where n is the quantum number. So, this is easily determined by your given function.

I am pretty certain that n,l,m = 3,1,0 for your given wave function. Here's an applet to check out the probability density:

http://www.phy.davidson.edu/StuHome/cabell_f/Density.html