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Introductory Physics Homework Help
QM, the convergence of the harmonic oscillator function.
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[QUOTE="BvU, post: 4991133, member: 499340"] Hello again, I'm pretty convinced you won't be pleased with this, but hear (read) me out... :) What matters here isn't the exact value of this a[SUB]k[/SUB] (or a[SUB]k+2[/SUB], for that matter), but the [U]ratio[/U] of these coefficients for really big k. Anything to do with the precise value can be swept in what Griffiths calls C ("for some constant C" -- anything you don't want to be bothered with: throw it in there. As long as it doesn't keep growing with k you're fine). Mind you, you want to be way above j = K/2 before you come even close to a[SUB]j+2[/SUB] / a[SUB]j[/SUB] ##\ \approx\ ## 2/j ! (I find I'm unconsciously switching to Griffiths' indices j now, sorry..)And even after all these years, I find it almost miraculous that from this kind of reasoning one is simply forced to conclude that K can NOT assume arbitrary values, but MUST be [U]exactly[/U] equal to 2j + 1 for some j, however big. A hair difference and the power series runs away like ##e^{x^2}##. Awesome ! [/QUOTE]
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Introductory Physics Homework Help
QM, the convergence of the harmonic oscillator function.
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