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How does planck's law require the absorbtion of light to be quantized? Planck's constant is simply a proportionality constant. A constant multiplied by a continuously variable quantity gives a continuously variable quantity. Where does quantization come in? Can someone please explain this one to me?

I guess I'm not understanding what is 'quantized' in the assumption of Planck's. The intensity of the radiation released at a given T and v? Or is it the energy of the radiation emitted at those frequencies? To what equation did Planck add a variable that can only take on integer values? The one for energy, intensity...I can't find it. I read his paper on quantization and he only meantions a constant, h, which by no means gives a discrete functional output. It gives a single number for each given T and v. Where is the mathematical manifestation of quantization in Planck's Law?

The harmonic oscillators were not individual atoms but groups of them.

So, the energy of the domains of atoms that are oscillating is quantized? The harmonic oscillators were not individual atoms but groups of them. That makes more sense. Using the bouncy ball analogy, several bouncy balls bouncing on parallel paths to each other generate the EM radiation? But, they can only generate EM radiation if they are bouncing with more than a certain threshold energy for each frequency, am I correct? That is, if the energy of the domain that is oscillating is equal to 5h then light will be emitted at E = 5h = hν => ν = 5 Hz? If that's true, then I think I finally understand!

I feel that for the broad spectrum case the concept of an "oscillator" is not a good one because this implies a long term periodic cyclic process. It is quite possible for electromagnetic quanta to be very brief just like a single pulse.

I guess I'm not understanding what is 'quantized' in the assumption of Planck's. The intensity of the radiation released at a given T and v? Or is it the energy of the radiation emitted at those frequencies?

Planck’s hypotheses was that the energy of a wave of a given frequency cannot be arbitrary but assumes only discrete values.

Lightarrow Fourier analysis is not relevant in this particular case.

This discussion brings me back to a question that I am still looking for a definitive answer to.Does an individual quantum posses bandwidth?

and is this a measurable property of a quantum?

However, there is probably much more to it than we are getting to in this discussion. The duality thing must come into it - if we are trying to discuss bandwidth then we are, by implication, talking about a wave - which is not the particle aspect of electromagnetism. Perhaps it's the wrong question to ask?

Because a photon has a finite effective lifetime and pulse length, it must have a bandwidth - it s bandwidth relates to the reciprocal of the length of the impulse of energy it carries.

McQueen you are wrong. All physical theories must be considered as approximations. Maxwells electromagnetic theory is perfectly adequate for many normal electromagnetic experimentation as is Newtonian gravity the additional theories of quantum mechanics and relativity are only needed for extreme cases where the accuracy of the theories breaks down.

Quote Because a photon has a finite effective lifetime and pulse length, it must have a bandwidth - it s bandwidth relates to the reciprocal of the length of the impulse of energy it carries. I am sorry I can’t understand this, a photon is supposed to have an infinite lifetime. That is if it is not absorbed it will maintain its energy, indefinitely.

Why? You know that it's possible to write every waveform, as short as you like, as an infinite sum of sinusoidal plane waves.

you have the interference pattern even sending individual photons; how would you interpret this fact?

QuoteWhy? You know that it's possible to write every waveform, as short as you like, as an infinite sum of sinusoidal plane waves.You should be more accurate if you want to get it right.Fourier ANALYSIS takes a repeating waveform and replaces it as an infinite series of harmonically related sinusoids. The Fourier TRANSFORM can be carried out on any function. The FT of a sinewave (in the time domain)which has been modulated by a pulse (i.e. a burst of sinewave) has a peak (in the frequency domain) at the 'carrier frequency' and, potentially, a continuum of sidebands (sinusoids of infinite duration) which stretch out on either side. The shorter the pulse in time , the more the spread of the sidebands in frequency.

Sure thing boss.