You are correct. Plane electromagnetic (EM) waves, such as light, do not have discrete energy levels like those found in systems with quantized energy, such as harmonic oscillators or atoms.
In classical electromagnetic theory, plane waves are described by continuous wave functions that can have any frequency and, consequently, any energy. The energy of a photon, which is the quantum particle associated with electromagnetic waves, is given by the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the wave. This equation shows that the energy of a photon is directly proportional to its frequency.
Quantization in the context of electromagnetic waves occurs during emission and absorption processes, where the energy is exchanged in discrete amounts corresponding to the energy of a single photon. These processes involve the interaction of electromagnetic waves with matter, such as atoms or electrons.
When an electron in an atom undergoes a transition from one energy level to another, it emits or absorbs a photon with a specific energy determined by the energy difference between the initial and final states of the electron. This emission or absorption process is quantized, meaning that only specific discrete energy levels are involved.
However, once emitted or absorbed, the photon itself behaves as a plane wave with a continuous spectrum of energies. It is only during the emission and absorption processes that the discrete nature of energy levels becomes apparent.
So, in summary, plane electromagnetic waves, including photons, do not have discrete energy levels in the same way that systems with quantized energy, like harmonic oscillators or atoms, do. The quantization of energy occurs during the emission and absorption processes, where the exchange of energy is restricted to discrete amounts corresponding to the energy of a single photon.