The REAL hydrogen atom


Q: What is the first derivative of psi?


Q: What is the second derivative of psi?


Q: Can you write the Schroedinger equation
   again, substituting in the values of the
   derivatives?


Q:  Using the first equation, find the value of "a".
    Evaluate it and find its value in meters.

However, note that this does NOT mean that the electron is always exactly the Bohr radius, as it would be in the Bohr model. Schroedinger's model of the atom provides only relative probabilities for the location of the electron. More on this tomorrow ....

That should look familiar ...

For example, here are illustrations of the solutions in the ground state, n = 1, first excited state, n = 2, and the second excited state, n = 3. Note that the size of the graphs changes!

For more information

You can view the solutions to the Schrodinger equation for the ground state AND a bunch of excited states by using Paul Fastad's hydrogen atom applet There's a local copy of the applet in case the network is flaky.
You can use a slightly different tool which shows hydrogen wave functions in a different manner on the Univ. of Alabama, Huntsville, Physics 113 page.
If you don't like applets, look at the pictures on the Hydrogen wavefunctions page from Daniel Finley's course at the U of NM.
There are more pictures at the QM supplement of the Chemistry Dept. at the U of Florida.