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I really need help understanding this equation ,i am new to quantum mechanics and i cant understand the math, so i need every single symbol to be explained or given a value if it is a constant , ( lets say X is Hydrogen) enter image description here

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What is the formula supposed to describe? What are the quantities involved? I can't make any sense about it without any additional information. –  Ondřej Černotík Jan 14 '13 at 17:13
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I don't really think you need to understand a lot of quantum mechanics to make sense of this. This is what I make of it:

$\phi_\infty(\lambda)$: The light intensity as a function of wavelength $\lambda$. Probably refers to the solar light before reaching earth's atmosphere.

$\exp\left[-\sum_m\sigma_m^{a}(\lambda)\int_z^\infty n_m(s)ds)\right]$: Factor representing the transmission of light throgh the atmosphere depending on wavelength. This is basically the Beer-Lambert Law with a summation over all absorbing species in the atmosphere and an integral along the light path.

$\sigma_m^{a}(\lambda)$: The absorption crossection of species $m$ at wavelength $\lambda$.

$n_m(s)$ : The number density (i.e. molecules per unit of volume) of species $m$ at point $s$ along the light path.

$\sigma_X^{(i)}(\lambda)$: Probably the photoioniztion crossection for $X$ at wavelength $\lambda$.

$n_n(X)$: Probably the number density of $X$.

The only thing that i find strange is that there is a sum over wavelengths. I would have expected an integral instead. But then I'm not used to notation and conventions for describing photoioniztion.

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