If one reads the current version of the wikipedia entry on Photoelectric_effect(adsbygoogle = window.adsbygoogle || []).push({});

we see that historically the postulate E=h f predates the relativistic theory. So it is kind of circular to argue in terms of [itex]E=h \nu[/itex] to justify [itex]E=h f[/itex]. The empirical process first postulated E=h f for the black body and then Einstein justifies the cut in the spectrum of the photoelectric effect by postulating a minimal non-zero required energy and that [itex]E = h \nu[/itex], being [itex]\nu[/itex] the frequency of the then-hypothetical quantum of electromagnetic radiation. The idea of light quanta began with Max Planck's published law of black-body radiation ("On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik 4 (1901)) by assuming that Hertzian oscillators could only exist at energies E proportional to the frequency f of the oscillator by E = hf, where h is Planck's constant.

Later on, Bohr suspects that the fundamental object to quantize is not the energy but the angular momentum. This rule works both for the 3D harmonic oscillator and for the Coulomb potential, and in this case it allows Bohr to calculate some of the spectrum of the hydrogen atom.

But it is important to reminder that E=h f as it is, for the harmonic oscillator, does not depend of relativistic formulae. Put V(x)= k x^2, solve the non relativistic Schroedinger eq, and you get E(n) = n h f + E(0).

A interesting related point, suggested by Okun, is that f is measurable in terms of space and time, while E seems to be more indirectly measured.

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# Energies and frequencies

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