How an Increase in r Affects the Appearance of Hydrogen Wave Functions

In a hydrogen atom, the wave functions change as you change the orbital radius, r. So what do the hydrogen wave functions look like? Given that

looks like this:

Here are some other hydrogen wave functions:

Note that

behaves like r^l for small r and therefore goes to zero. And for large r,

decays exponentially to zero. So you’ve solved the problem of the wave function diverging as r becomes large — and all because of the quantization condition, which cut the expression for f(r) from an exponent to a polynomial of limited order. Not bad.

The radial wave function R₁₀(r).

You can see the radial wave function R₁₀(r) in the first figure. R₂₀(r) appears in the second figure. And you can see R₂₁(r) in the last figure.

R₂₀(r).

R₂₁(r).