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**New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?**

« **on:**30/05/2023 16:12:29 »

Hi.

I've always thought that Quantisation is fairly odd and can only be used with caution. Although we can use Quantum mechanics to establish that quantisation should be there, we then quickly establish that we cannot observe a perfect example of it. Instead what we will typically observe is a frequency that could fall anywhere within some continuous range, with just some statements we can make about the probability distribution or spread of what is typically a continuous random variable.

An atom with an electron in an excited state, should eventually have that electron fall back to a lower energy orbit but we don't really know exactly when that will happen. Although the transition from one orbit to another should be quantised, there is an uncertainty relation between the time the atom takes to transition (remains in the excited state before falling back to the lower energy state) and the energy of the photon released.

See https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.03%3A_The_Heisenberg_Uncertainty_Principle

for some discussion (especially the section around equation 7.3.2 and example 7.3.3).

As a consequence, all atomic spectral emission / absorption lines have some non-zero width rather than being perfect spikes at precisely one frequency. There is another theoretical limitation that can be considered: We also have a position - momentum uncertainty relation. The atom which emitted the photon along with the detector that captured and identified it can be moving relative to the lab frame and a Doppler-shift in frequency is inevitable.

In practice there are also limitations on the accuracy of the equipment and random experimental errors that appear. Even if you overlook those experimental limitations, the theoretical limitations from uncertainty relations cannot be avoided. Overall, there should be some precise quantisation BUT you can't observe it in any single measurement. Theoretically, we can only assert that the expected frequency of a photon emitted by an excited atom should correspond to the difference in the energy between the two states of the atom. There is nothing we can do to remove all of the randomness and spread of the actual frequency that is really detected from any one atom and one emission.

Best Wishes.

I've always thought that Quantisation is fairly odd and can only be used with caution. Although we can use Quantum mechanics to establish that quantisation should be there, we then quickly establish that we cannot observe a perfect example of it. Instead what we will typically observe is a frequency that could fall anywhere within some continuous range, with just some statements we can make about the probability distribution or spread of what is typically a continuous random variable.

An atom with an electron in an excited state, should eventually have that electron fall back to a lower energy orbit but we don't really know exactly when that will happen. Although the transition from one orbit to another should be quantised, there is an uncertainty relation between the time the atom takes to transition (remains in the excited state before falling back to the lower energy state) and the energy of the photon released.

See https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.03%3A_The_Heisenberg_Uncertainty_Principle

for some discussion (especially the section around equation 7.3.2 and example 7.3.3).

As a consequence, all atomic spectral emission / absorption lines have some non-zero width rather than being perfect spikes at precisely one frequency. There is another theoretical limitation that can be considered: We also have a position - momentum uncertainty relation. The atom which emitted the photon along with the detector that captured and identified it can be moving relative to the lab frame and a Doppler-shift in frequency is inevitable.

In practice there are also limitations on the accuracy of the equipment and random experimental errors that appear. Even if you overlook those experimental limitations, the theoretical limitations from uncertainty relations cannot be avoided. Overall, there should be some precise quantisation BUT you can't observe it in any single measurement. Theoretically, we can only assert that the expected frequency of a photon emitted by an excited atom should correspond to the difference in the energy between the two states of the atom. There is nothing we can do to remove all of the randomness and spread of the actual frequency that is really detected from any one atom and one emission.

Best Wishes.

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