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The concept of Energy Spectral Density is a little nebulous

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EPalomo:
Hi! I'm taking P Chem II right now and we've just started our intro to quantum mechanics. The definition our book gives for Energy Spectral Density isn't the most helpful, so I was wondering if someone would be able to help me get a better grip on the concept? I'd really appreciate it.

So far I understand it as the distribution of energy within a specified range of wavelengths. Like if a blackbody is radiating energy away from itself at a constant temperature, the Energy Spectral Density would be a range of wavelengths that each carry unique amounts of energy away from the blackbody which are different from one wavelength to the next, with some carrying more energy away from the blackbody than others. Is this heading in the right direction or am I still pretty lost? Thanks again!

Corribus:
More or less correct. The density here refers not to a mass density but a density along the frequency (or wavelength) axis. Just bear in mind that the energy of a photon is related to it's frequency, and the total energy emitted at that frequency is scaled by the number of photons at that frequency. When you take those two ideas together, and plot as a function of amount of energy emitted as a function of frequency, that's essentially your energy spectral density. Note that the energy spectral density is expressed at an instant of time. A related concept, power spectral density, averages the energy spectral density over long periods of time (power = energy/time).

EPalomo:

--- Quote from: Corribus on January 22, 2021, 09:59:18 AM ---More or less correct. The density here refers not to a mass density but a density along the frequency (or wavelength) axis. Just bear in mind that the energy of a photon is related to it's frequency, and the total energy emitted at that frequency is scaled by the number of photons at that frequency. When you take those two ideas together, and plot as a function of amount of energy emitted as a function of frequency, that's essentially your energy spectral density. Note that the energy spectral density is expressed at an instant of time. A related concept, power spectral density, averages the energy spectral density over long periods of time (power = energy/time).

--- End quote ---

Thank you! I think part of my trouble was that I'm used to conceptualizing density in a "mass per unit volume" sense, which is a little too narrow. Would it be accurate to summarize this as "the quantity of photons per frequency/wavelength is the result of the amount of energy emitted at that frequency/wavelength"?

I'm also realizing that my perception of ESD was initially too focused on the wavelengths themselves rather than the energy being carried by the photons.

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