When a quantum mechanical Hamiltonian cannot be solved exactly, one can estimate system energies with a technique called the variational method. The idea is to calculate the energy expectation value for a trial wavefunction with one or more tunable parameters and determine the minimum energy that results from varying the parameters. As an exercise to help his students get a feel for the approach, the University of Rochester’s Carl Hagen applied it to a solvable system—the hydrogen atom. With the help of Rochester colleague Tamar Friedmann, he found to his surprise that the exercise yielded a representation for published in 1655 by mathematician John Wallis:
Hagen and Friedmann considered a trial wavefunction that had the same angular behavior as the hydrogen atom but different radial behavior....
