4.1.4.3 Solution harmd-c

**Question:**

Write down the explicit expression for the eigenstate

**Answer:**

The generic expression for the eigenfunctions is

and substituting

Now substitute for those functions from table 4.1:

where the constant

The first polynomial within square brackets in the expression above is zero at

Seen from above, you would see four rows of three patches, as the third polynomial between brackets produces zero probability of finding the particle at

This example illustrates that there is one more set of patches in a given direction each time the corresponding quantum number increases by one unit.