From quantum physics, I would expect that seeing e.g. red would excite the 564nm energy level of the Photopsin protein. I would also expect to only see (apart from some small smeering out) that we are only able to see 564nm. But based on this spectrum from Wikipedia
the opsine absorption curve is a quite spreaded bell-shaped curve.
Why do the proteins in our eye have a continuous (bell-shaped) absorption spectrum and why are they less sensitive to higher energetic photons?
What makes you think that the smeering out you would expect from the answer given by user Terry Bollinger would be small? Indeed,
when the target receptor is sufficiently large and complex to absorb whatever the difference is between the light that was emitted and atomic-level receptors of the target. A good example of this kind of flexible absorption is the opsin proteins in the retina of your eye. These proteins are sufficiently large and complex that, like pitcher's mitts in baseball, the molecule as a whole can absorb the mismatches energy, momentum, and spin of any photon that falls within a certain rather broad range of frequencies and polarizations.
... answers your question as well.
To be more specific, this effect being described by Terry is the sum of factors known togther as spectral broadening, or line broadening, and in the specific case of opsin I believe the main contributors will be Quasistatic Pressure Broadening and Thermal Doppler Broadening. You should expect a normal distribution in the broadening caused by these two factors, and for a molecule as large and complicated as opsin a standard deviation of hundred of nanometers is also expected from these effects.
You can read more about spectral broadening in general, the exact mechanism for pressure and thermal broadening, as well as other mechanisms responsible for broadening in other cases, here.
An organism whose spectral sensitivity had gaps in it would be blind to colors whose wavelengths fall in those gaps. Not color-blind like humans who have two opsin proteins instead of three, so that e.g. red and green are indistinguishable, but blind: those colors would be invisible. For our visual system, a prism refracting sunlight onto a dark wall makes a continuous smear of light. But for an organism with gaps in its spectral sensitivity, that spectrum would have dark regions where the available light had invisible wavelengths.
This gives a biological answer to your question: the broader the spectral response of an opsin protein, the more useful it is. This suggests that any independently-evolved photochemical should be a big floppy molecule whose photon-absorbing states merge into a continuum, as described in the excellent answer that you linked.
Note that most sighted non-mammalian animals have four opsins, rather than three. Mammals are all a little color-blind compared to birds, reptiles, and most fish. An interesting question is whether there are any animals whose visual systems have color insensitivities in the middle of their visual spectrum. It's interesting to imagine the experience of being blind to the color blue (but not purple, green, yellow, red) in the same way that we are blind to ultraviolet and infrared.
