How can energy be quantized with E=hv

vanesch

Yes.

vanesch

Yes. (for an unbound system).

vanesch

I would like to make a general comment: in many scientific disciplines, but especially in quantum mechanics, there are many "catch phrases" which are correctly and succinctly summarizing a certain property/phenomenon/event/view/... in a given context, but which are then thrown around in all generality and stated as "general truths" or "principles", especially in introductory and popularizing texts. It is my impression that they add more to confusing than anything else. "energy is quantized" is one of those catch phrases. There are many others floating around in "quantum speak". If you know what they mean exactly, then they are right, but usually one needs a much deeper understanding of quantum mechanics than is available to the reader to which one gives these "one-liners", and then they are genuinely confusing.

mahela007

Bravo Vanesch... you hit the nail right on the head.
Well.. as for my little problem, it's been solved. Thanks for your help.

Halcyon-on

True! Physics is done using the mathematical language. When mathematical concepts are translated in ordinary words, it is inevitable to generate misunderstandings.

Uli

[QUOTE=mahela007;2354585]I don't understand how Planck's equation can state that energy is quantized.
in E = hv where E = energy of the photon h Planck's constant and v=frequency how can E have only discrete amounts?

plancks constant is .. well.. a constant but isn't frequency a constantly varying or Infinitely variable quantity? If so, how can E have only certain values?

You can build an oscillator with a constantly varying frequency but only certain frequencies can be absorbed or emitted by atoms and these are defined by the spectral lines of the atoms. This means that an atom can only absorb energy tied to fixed frequencies and the amount of energy is given by E=hv.

alxm

The energy of a photon can have any value.

The fact that atoms can only emit or absorb photons with some values doesn't mean photons with other values can't exist.

lightarrow

What does it mean exactly? Of course it doesn't mean that you can accelerate a free photon...

vanesch

It means that there exist free photon states of all energies (in other words, that the energy spectrum of the free EM field is continuous).

lightarrow

Thanks vanesh.

burningbend

really, E=hf shouldn't be thought of as a pure quantum rule. it's a way to relate frequency to energy and not a statement about any specific state or set of states in an atom. basically that equation is used once we figure out either the energy or the frequency of a transition between quantum states so that we can find the other value. no inference can be taken because of the equation.

i hope that's a little bit simpler language than the rest of the thread.

lightarrow

I ... almost completely agree. Not totally, because:
starting from electromagnetic (classical) Doppler shift, you can find that the em energy transforms, under a velocity boost, in a certain way, which becomes exactly E = hf under the hypothesys that the field is made of energy "packets"; the energy arriving to a detector depends on the energy of the single packet and on the number of packets arriving and this number, as the frequency, depends on the relative velocity v between source and detector.
Probably there is a simpler way to say that using 4-vectors, anyway, the simple fact that E = hf, is *almost* a prove that the field's energy comes in "packets".