<p>In this manuscript, I speculated that the energy density
distributions along space and time in a quantum system are uniform. Thus, the
complementary energy contributions are added to the classical solutions of the
1D particle in a box problem, making the energy density a complex distribution
function over space and time. Then the concept is extended to the free rotation
problem with a Hamiltonian slightly different than the classical Schrödinger
equation. The picturized energy distribution functions and associated time
evolution are described in movies for comparison between example classical wave
functions and the energy density functions. The wave functions for the hydrogen
atom are then guessed based on the historical solutions.</p><p><br></p>