From: richalivingston@gmail.com   
      
   On Monday, May 30, 2022 at 4:06:45 AM UTC-5, Lou wrote:   
   > 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?   
      
   At first I thought the answer was obvious, but then I thought about it a little   
   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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