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May 30, 2022, 5:06:45 AMMay 30

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We are all familiar with the equations to quantify energy of EMR from a

single wavelength or frequency. But I have been unable to find any

reference on how to calculate energy from a *range* of wavelengths or

frequencies. In particular with reference to Doppler shifted emr For

instance: Can one calculate what difference in energy , if any, an

emitted source of emr between 100-200nm would have if it was redshifted

to 200-400nm?

single wavelength or frequency. But I have been unable to find any

reference on how to calculate energy from a *range* of wavelengths or

frequencies. In particular with reference to Doppler shifted emr For

instance: Can one calculate what difference in energy , if any, an

emitted source of emr between 100-200nm would have if it was redshifted

to 200-400nm?

May 30, 2022, 2:41:13 PMMay 30

to

more and realized I needed to think about it more carefully.

It is easiest to think of this quantum mechanically, I think. The number of

photons does not change, but their rate is reduced proportional to the

frequency. This gives a factor of 1/2 to the rate of photons. In addition

each photon is now half the frequency, so the energy per photon is also

reduced by 1/2. So the total power in the band 200-400nm would be 1/4

the power in the 100-200nm band prior to being red shifted.

Doing this calculation in classical EM would require transforming the EM

tensor F^{\mu\nu} via the Lorentz transform to get the correct EM field

amplitudes, from which the energy density can be calculated. The QM

argument is much simpler.

Rich L.

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