(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a two-level atom with transition frequency [tex]{ \omega }_{ ji } \equiv { \omega }_{a}[/tex] and spontaneous decay rate [tex]\gamma[/tex], we are asked to find an expression for the "power spectral density function" [tex]S(\omega)[/tex], in terms of [tex]\omega, {\omega}_{a}[/tex], and [tex]\gamma[/tex].

2. The attempt at a solution

Of course, it should be normalized to 1,

[tex] \int_{- \infty }^{ \infty } d \omega S(\omega) = 1[/tex]

I believe that the PSD function is just a Fourier Transform of the decay rate, right? If so,

[tex]S(\omega)= \frac{ 1}{ \sqrt[ ]{ 2 \pi } } \int_{ - \infty }^{ \infty } \gamma (t) { e}^{ - \imath \omega t} dt[/tex]

And then I would just need to double-check that it's normalized.

Thoughts on this?

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# Help with Power Spectral Density Function derivation

Can you offer guidance or do you also need help?

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