Suppose We Have a Quantum System of an Unknown Type $\Delta E$

Multiple Choice

Suppose we have a quantum system of an unknown type. We find that a certain amount of energy $\Delta E$ moves this system from its lowest possible energy to its second-lowest energy, but $\frac{5}{27} \Delta E$ is required to get it to its next higher energy. Is this quantum system a quanton in a box, a hydrogen atom, or a simple harmonic oscillator?

A) A quanton in a box.
B) A hydrogen atom.
C) A simple harmonic oscillator.
D) The stated facts are inconsistent with all of these models.