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 May 25th, 2018, 12:19 AM #1 Newbie   Joined: Dec 2016 From: Scotland Posts: 5 Thanks: 0 Rearrangement from Quantum Mechanics I am trying to rearrange this equation but I just cant figure out how change the first term: $$-\frac {1}{2} \frac {1}{r^2}\frac{\mathrm{d} }{\mathrm{d} r}\left (r^2\frac{\mathrm{d} }{\mathrm{d} r} R(r) \right ) - \frac {z}{r}R(r) = ER(r)$$ Using the relation: $$U(r) = R(r)r$$ $$-\frac {1}{2} \frac{\mathrm{d^2} }{\mathrm{d} r^2}U(r) - \frac {z}{r}U(r) = EU(r)$$ Any help would be really really appreciated. May 25th, 2018, 03:29 AM #2 Senior Member   Joined: Jun 2015 From: England Posts: 915 Thanks: 271 OK so you have (I have not bothered with R(r) or U(r)) $\displaystyle U = Rr$ given or $\displaystyle R = \frac{U}{r}$ (useful in later substitution) Differentiate the first as a product with respect to r, since you have the product of two functions of r $\displaystyle \frac{{dU}}{{dr}} = r\frac{{dR}}{{dr}} + R.1$ rearrange $\displaystyle \frac{{dR}}{{dr}} = \frac{1}{r}\frac{{dU}}{{dr}} - \frac{R}{r}$ substitute second equation $\displaystyle \frac{{dR}}{{dr}} = \frac{1}{r}\frac{{dU}}{{dr}} - \frac{U}{{{r^2}}}$ Now can you substitute these results into your main equation and continue to the desired result, performing the second differentiation and some algebra? Thanks from Benit13 Last edited by studiot; May 25th, 2018 at 03:32 AM. May 25th, 2018, 04:04 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 $\displaystyle \frac{d}{dr}\left(r^2\frac{d}{dr}R\right)= r^2\frac{d^2R}{dr^2}+ 2r\frac{dR}{dr}$ so $$\frac{1}{r^2}\frac{d}{dr}\left(r^2\frac{d}{dr}R \right) = \frac{d^2R}{dr^2}+ \frac{2}{r}\frac{dR}{dr}$$ Last edited by greg1313; May 25th, 2018 at 05:04 PM. Tags mechanics, quantum, rearrangement Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post SenatorArmstrong Physics 2 October 16th, 2017 10:00 AM Andrzejku98 Linear Algebra 3 March 12th, 2017 02:22 PM VisionaryLen Physics 10 September 12th, 2016 04:03 AM humbleteleskop Physics 17 July 25th, 2015 03:38 AM JDA Applied Math 1 November 26th, 2007 01:52 AM

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