Spectrum Continuity: Quantum & Real-Life Perspectives

[Small bugs]

Now that, in bound state, the particles have quantized energy. So the system can only absorb certain kinds of photons. But why when I see the absorption graphic in books(x-axis is wavelength; y-axis is intensity, transmission percentage or sth), they are all continuous? They do have peaks, though, why at other wavelengths, there is still some amount of intensity? Why they are not 0 or nearly equal to 0?
E.g. the CO O₂ rotation-absorption spectrum.
https://www.mecheng.osu.edu/netl/vibrational-energy-storage-high-pressure-gas-mixtures
Is there existing other mechanism that let the system absorb photons continuously?
I meant generally, why in quantum world it is quantized, but the in real life it is still continuous?

 

[blue_leaf77]

These are the effects of spectral line broadening. There are various mechanisms that prevent the observation of spectral line to be perfectly discrete, e.g. natural broadening which results from spontaneious emission causing the state lifetime to be finite, collision broadening, and Doppler effect. A treatment of each of these broadening may be found in many textbooks on solid state physics or lasers, the following link may also be interesting to you if you are only interested in a summary http://www.phy.ohiou.edu/~mboett/astro401_fall12/broadening.pdf. Spectrometer resolution may also play a role in the broadened appearance of those lines.

 

[Small bugs]

These are the effects of spectral line broadening. There are various mechanisms that prevent the observation of spectral line to be perfectly discrete, e.g. natural broadening which results from spontaneious emission causing the state lifetime to be finite, collision broadening, and Doppler effect. A treatment of each of these broadening may be found in many textbooks on solid state physics or lasers, the following link may also be interesting to you if you are only interested in a summary http://www.phy.ohiou.edu/~mboett/astro401_fall12/broadening.pdf. Spectrometer resolution may also play a role in the broadened appearance of those lines.

Thx. Still a problem with transition and life time.
And with which equations can we calculate the life time and transition probability? Time-dependent Schrödinger equation? But for time-dependent S equation, it seems that the system will never transit and just be in superposition forever.
How can we know how long is will it transit to other energy level. Or in QM, we can not say exactly how long, so how can we predict the transition?

 

[DrClaude]

Thx. Still a problem with transition and life time.
And with which equations can we calculate the life time and transition probability? Time-dependent Schrödinger equation? But for time-dependent S equation, it seems that the system will never transit and just be in superposition forever. How can we know how long is will it transit to other energy level. Or in QM, we can not say exactly how long, so how can we predict the transition?

You need to consider the coupling between the molecule and the electromagnetic vacuum field. That will give an exponentially decaying probability of finding the molecule in the excited state.

 

[blue_leaf77]

The accepted treatment of spontaneous emission, a process responsible for natural broadening, is found in quantum electrodynamics. Indeed, if you consider an excited state in QM, it will not decay by any means unless a perturbation is applied, so QM cannot explain satisfactorily the natural broadening. Nevertheless, the spontaneous emission rate can be well estimated using Fermi's golden rule which is derived in the frame of QM https://en.wikipedia.org/wiki/Spontaneous_emission.