Why does $hf$ in Planck's formula imply quantization? It can be a very naive question, but I came across a textbook saying:

$hf$ suggests that the energies of the atomic oscillators in the cavity wall are quantized.

But I don't get the why. I already read two threads here and here but I don't think the straight answer my question even though the answers mentioned the fact that $hf$ implies that the energy is quantized. I don't need a historical viewpoint, just the physics of why $hf$ involves quantization of energy.
 A: It appears in how the equation is interpreted. $E = hf$ means that the quanta of energy for a wave of frequency mode $f$ is $E$. The total energy content in a beam or the power radiated and so on, has to do with the amplitude or the intensity etc. However, that energy must be split up into quantas or small chunks of energy $E$, and isn't transmitted continuously. 
The equation doesn't just "involve" quantization, it is the definition of exactly how energy is quantized.
A: E=hf does not in itself imply quantisation. HISTORICALLY the formula was first associated with Einstein's interpretation of the photo-electric effect. Classical mechanics suggested that the EM wave continuously imparting energy to atoms etc. Instead, the electron were ejected the moment the light source was switched on as if knocked off the atoms by high-speed particles of light (photons). The energy the electrons received implied the photons had energy E=hf.
A: Nowadays $E = hf$ is seen as a statement about photons of frequency $f$, but the quotation you give is clearly in the context of Planck's explanation of the spectrum of blackbody radiation. Historically Planck did not actually assume quantization of the electromagnetic field itself, that had to wait till 1905, with Einstein's explanation of the photoelectric effect.
To get to Planck's formula for blackbody radiation, which was empirically obtained, you don't have to assume quantization of the energy states of the oscillators that the cavity wall is built out of, nor of the electromagnetic field, you only require that energy exchange between the matter and the radiation is quantized. 
However, it seems that Planck did just this, he postulated that the physical oscillators at a given frequency could only be in one of a discrete set energy states of energy $nhf$, where $n$ is an integer and $h$ a constant. From this he concluded that energy exchange between the matter and the radiation at a given frequency $f$ could only be in multiples of $hf$, from which a formula could be obtained that was in excellent agreement with experimental data.
So


*

*If your context is that energy exchange for radiation of a given frequency can only be in multiples of $hf$, then for someone in 1900 this could have suggested that the oscillators of a given frequency $f$ of the cavity wall can only be in states that have quantized energy.

*Historically I think this was the other way around: first the assumption on the oscillator states was made, then from that the energy exchange quantization followed.

*Once you allow the electromagnetic field itself to be quantized, you don't need to assume quantization of the oscillator states.


So I would say, it may indeed suggest the quantization of the oscillator states, but that is not an inevitable conclusion.
