OK, let me explain a bit better. The ground and 1st excited states of an Hydrogen atom are often given as an example of a qubit for use in quantum computing. The energies of these states are definitely eigenstates of the Hamiltonian. My question has to do with an Hydrogen qubit in a superimposed state comprising both the ground and 1st excited state. If this qubit has been altered via a quantum algorithm, then one would like to measure the probabilities that it is in state |0> or state |1>. How could this be done?
Of course this measurement would have to be re-done multiple times to arrive at an estimation of the probabilities.