Quantization of the energy

[@whatitmeans]

min 7:25: "... so the requirement that the solution {of the time independent Schrödinger equation for the harmonic oscillator} be normalizable quantizes the energy".... amazing.

[@zelinma2403]

Thank you very much professor Zwiebach. Finally understood the quantized energy of SHO

[@whatitmeans]

something I don't fully understand is the following: if the solution is normalizable, then it must have in principle a bounded spectrum due the Riemann-Lebesgue Lemma, right?... it kind of fit with the ultraviolet catastrophy phenomena, but I have never seen an explanation about how this lemma should limit the maximum frequency a photon can have. Dou you have any sources relating the Riemann-Lebesgue Lemma to Quantum systems?

[@whatitmeans]

I have another question, since looks I misunderstood something important: Does not truncating the coefficients of a power series just make it a simple polynomial (so impossible to normalize)??!!

[@gmcenroe]

Good lecture but it would have been nice to take the time to show how we arrive at the recursion relation as he did when he substituted for the 2013 Physics 8.04 class that Allan taught.

[@rakhuramai]

for that you can watch the previous video in the playlist this video is from

[@Iceyer-su1et]

I apologize for the inconvenience, but I would like to know if anyone can provide a clear and insightful video, book, or article to explain what exactly the 'generating function' mentioned in the course is?

[@mitocw]

See the course materials for more info at ocw.mit.edu/8-04S16. The syllabus, calendar, and lectures notes should help you out. Best wishes on your studies!

[@bobytrust8822]

Can drive the formula (E/square C) Times Square root of -1(PV/nR)

[@not_amanullah]

Thanks ❤️🤍

[@dorysouza1770]

Oh my... this is a beautiful lecture. The book material could be better to explain these arguments, thanks.

[@kingofAvalon]

Great

[@brainstormingsharing1309]

👍👍👍👍👍👍👍👍👍

[@SampleroftheMultiverse]

Thanks for your video. Your viewers might enjoy seeing this visual aid. The sheet of spring steel buckled to a Gaussian curve represents a two dimensional field with the ends bounded. Seeing the mechanical effect takes some of the mystery of what the math is showing. Your viewers might be interested in watching the test video of the model. See the load verse deflection graph. kzbin.info/www/bejne/raOlpKSfepWpfZYsi=waT8lY2iX-wJdjO3