Just to emphasize an aspect of John D. wrote about; quoting only in part:
"To cut to the chase: Non-experts like to say that energy is quantized.
They take this as the defining property of energy and/or the defining
property of quantum mechanics. The problem is, it's just not true.
Note the contrast:
-- If you decide to measure the atom by projecting it onto the energy
eigenstate basis, then sure, the energy will be quantized.
++ However, the energy states are not the only states. They are not
even the only basis states!"
I'd point out that there are systems where the energy isn't even discretely quantized. Energy eigenstates of the free electron,
for example, display a continuum of possible energy values, just as in Classical mechanics.
Discretely quantized energy states; is not a necessary property of a quantum system.
By quantum system I mean a physical system not amenable to description by Classical Mechanics to a reasonable degree of accuracy.