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The Secret of Oscar's Intensity: What It Reveals about the Mysterious Interaction between Light and Matter?
In physics, Oscar intensity allows us to peer into the fundamental interactions between light and matter. Once we understand this quantity, we can better understand how the absorption or emission of light occurs through changes between energy states of atoms or molecules. This not only allows us to explain various phenomena in nature, but also plays an important role in many scientific and technological applications.
The Oscar intensity is a dimensionless quantity that expresses the probability of absorbing or emitting electromagnetic radiation when transferring between atomic or molecular energy levels.
For example, if the Oscar intensity of a radiative state is small, nonradiative decay will exceed radiative decay. Conversely, "bright" transfers have greater Oscar intensity. Additionally, the Oscar intensity can be viewed as the ratio of this quantum mechanical transfer rate to the classical absorption/emission rate of an electronic oscillator with the same transfer frequency.
The definition and formula of Oscar intensity
An atom or molecule can absorb light and change from one quantum state to another. For a certain transition from a low state |1 to a high state |2 , its Oscar intensity f_{12} can be defined as:
f_{12}={\frac {2}{3}}{\frac {m_{e}}{\hbar ^{2}}}(E_{2}-E_{1}) \sum _{\alpha =x,y,z}|\langle 1m_{1}|R_{\alpha }|2m_{2}\rangle |^{2}
Among them, m_{e} is the mass of the electron, and \hbar is the reduced Planck constant. The Oscar intensity is the same for every substate |nm_n .
Thomas-Lesch-Kuhn sum rule
In order to make the above equation applicable to the continuous spectrum state, the matrix elements need to be rewritten. In the absence of a magnetic field, the Hamiltonian can be written as:
H={\frac {1}{2m}}{\boldsymbol {p}}^{2}+V({\boldsymbol {r}})
And calculate the exchange relationship between operators and position variables to obtain the relationship between states. This allows us to derive the Thomas-Leich-Kuhn summation rule, which helps understand how the interaction of light with matter affects the probability of electron transfer.
Application in crystals
In crystals, the energy spectrum of electrons has a band structure. When approaching the minimum value of each energy band, the electron energy can be expanded by various powers of momentum
p
. This works because the electron mass is effective massm^{*} in different energy bands, which affects its Oscar strength.
The ratio of the free electron mass
mto its effective mass in the crystalm^{*}can be thought of as the electron transfer from the bottom quantum state of the n-band to the same Oscar intensity of state.
This explains how electrons in different energy bands are affected, showing how the interaction of light and matter at the microscopic level shapes the phenomena we observe.
Summary
As an important tool to explore the interaction between light and matter, Oscar intensity is crucial in both basic science and applied technology. By understanding Oscar intensity, we can uncover the mysteries hidden between light and matter and advance our understanding of the natural world. However, what undiscovered secrets does such a basic physical quantity hide?
