A few years ago I attended a talk given by Andy Strominger entitled Black Holes- The Harmonic Oscillators of the 21st Century. This talk, http://media.physics.harvard.edu/video/?id=COLLOQ_STROMINGER_091310 was quite formidable and has had a lasting impression on my physics studies since. I'd consider the talk transformative in my approach. Now, imagine hearing the power of the harmonic oscillator model for the first time before taking an EM or QM class and simply having a spring mass system in mind...
Fast forward a few years and consider learning the eigenfunctions of the harmonic oscillator Hamiltonian ${\Omega_n}$ are an orthonormal basis set for $\mathcal{H}=L_2(\mathbb{R^d},d\mu)$. A statement equivalent to:
1) Schwartz Space $\mathscr{S}$ being Fourier invariant
2) The Fourier inversion theorem holding
Now, the power of the harmonic oscillator is coming to fruition in what I can solve in physics. Admittedly, there is still much in the field that is beyond me at this point that is well represented by the harmonic oscillator model.
This leads me to first ask what are the best known fits for the harmonic oscillator model?
However, this question is not the main focus of this post as I am also deeply interested in models extending beyond the harmonic oscillator paradigm. Namely, what are examples of objects currently being modeled as Black holes? It's interesting (for me, hopefully more) to ask this question in the "firewall" era, given that I attended this talk before the now famous AMPS paper.
So, in summary I am asking for examples of physical objects modeled by harmonic oscillators, or black holes, relevant in the field today. It would be interesting to compare the usage of the models in light of the theme of Andy Strominger's talk.
