Graduate What is the true energy required to excite an atomic electron?

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The discussion centers on the energy required for electronic excitation of an atom, defined as Planck’s constant multiplied by the frequency of waves per second. It highlights that electronic excitation occurs on a time scale much shorter than one second, raising questions about whether excitation is due to a single wave or multiple waves. A complete understanding of this process involves quantum field theory (QFT) and the quantization of the electromagnetic field. While a basic quantum mechanics (QM) approach describes the absorption and emission of a single photon, this simplification does not capture the full complexity of atomic excitation. The conversation emphasizes the need for a deeper analysis beyond basic QM to fully explain the phenomenon.
Maurice Morelock
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Is electronic excitation caused by a single wave or multiple waves in a given time period?
Energy is equal to Planck’s constant times the number of waves in 1 sec. The time scale for electronic excitation is far shorter then one second. So when we talk about the excitation of an electron from a lower level to a higher level occurring at a certain energy, are we talking about the exciting photon as a single wave with the amplitude equal to the number of waves in one sec?
 
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Maurice Morelock said:
Summary:: Is electronic excitation caused by a single wave or multiple waves in a given time period?

Energy is equal to Planck’s constant times the number of waves in 1 sec. The time scale for electronic excitation is far shorter then one second. So when we talk about the excitation of an electron from a lower level to a higher level occurring at a certain energy, are we talking about the exciting photon as a single wave with the amplitude equal to the number of waves in one sec?
A full description of the excitation of an atom by a photon requires an analysis using QFT and, in particular, the quantization of the EM field.

https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field

The simplest description using only QM has a single photon of precisely the correct energy being absorbed by the atom and then a photon of the same energy being subsequently emitted. This is, however, not the whole story.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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