What Can the Wave Function for Hydrogen Tell Us About Its Properties?

[jg370]

Homework Statement

Suppose a hydrogen atom is in the $$2s$$ stat, with its wav function given by:

$$\psi_2_s (r) = \frac{1}{4\sqrt(2\pi a_o^\frac{3}{2})} (2-\frac{r}{a_o}) e^(-\frac{r}{2a_o})$$

Taking $$r = a_o$$, calculate $$\psi_2_s (a_o)$$

Homework Equations

The Attempt at a Solution

Since $$r=a_o=0.0529 nm$$, I get $$\frac{1.57*10^(14)}{ m^3}$$

Now, my question is "what is the meaning of this value?

 

[Redbelly98]

Well, the units of a 3-D wave function should have m^3/2 in the denominator (i.e. the units are m^-3/2).

I'm not sure people actually ascribe physical meaning to the value of a wavefunction. I think of wavefunctions as a calculational tool in determining observable quantities such as position, momentum, energy, etc. QM is all about measurable quantities or observables.

Hope that helps.