We know that a quantum state is more unlikely if it is in a higher energy state. Does there exist a general rule for how probability amplitude is determined via energy levels?
If for a Hydrogen atom, all we know is that it is in a first excited state, we can say that it is equally likely to be in $2S$, $2P_{x}$, $2P_{y}$, and $2P_{z}$ states (small corrections ignored). But if all we know is that there are a total of $n$ energy states with corresponding energies, could we deduce the probability amplitude from the energy levels to write down a general normalized wave function?
