Quantum physics says that energy is quantised, and since the energy of a photon is only dependent on the wavelength, the wavelength of a photon is quantised. This means that even though an infinite amount of numbers exist between 380 and 700, there is a finite amount of wavelength a photon can have between 380nm and 700nm.
1) How can I mathematical predict if it is possible for a photon to have a given frequency?
2) How many possible frequencies can a photon have within the visible spectum?
3) In general, in there an equation for how many possible frequencies a photon can have within any given range?
Edit: I managed to find an answer on Hyperphysics. "[T]he frequency available [for a photon of light] is continuous and has no upper or lower bound, so there is no finite lower limit or upper limit on the possible energy of a photon." I think that what it is meant when physicists say 'energy is quantized' is that particles of matter have quantized energy levels, but the energy levels of particles carrying energy between that matter (e.g. photons) are not quantized.
