Timeline for How can I derive the relationship between the scattering phase shift, the potential, and the radial eigenfunctions?
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| Feb 7, 2023 at 4:10 | history | edited | Qmechanic♦ |
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| Jan 24, 2023 at 5:48 | history | edited | Marcellus | CC BY-SA 4.0 |
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| S Jan 21, 2023 at 11:07 | history | edited | John Rennie |
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| S Jan 21, 2023 at 11:07 | history | suggested | SCh |
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| Jan 21, 2023 at 5:55 | review | Suggested edits | |||
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| Jan 21, 2023 at 5:50 | history | edited | Marcellus | CC BY-SA 4.0 |
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| Jan 21, 2023 at 5:44 | answer | added | Marcellus | timeline score: 1 | |
| Jan 19, 2023 at 5:51 | comment | added | Marcellus | I checked section 9.1 of the Cal Tech reference that you provided and that indeed was what I was looking for. Thank you! The reason the exponential factor on the LHS in Merzbacher's equation is not present is that he included it in the wave function term on the RHS so it cancels out of the equation. I greatly appreciate your taking the time to find this for me. | |
| Jan 16, 2023 at 19:03 | comment | added | Marcellus | I can see why you might say that since those factors are often seen together, but in this instance there is only the sine term. I'm eager to check the reference you mentioned, but I'm traveling today and have only poor internet service. I appreciate your interest. | |
| Jan 16, 2023 at 6:50 | comment | added | Ghoster | I don’t have a copy of Merzbacher. Did you leave out a factor of $e^{i\delta_l}$ on the left side of (11.83)? | |
| Jan 15, 2023 at 8:39 | comment | added | Ghoster | I think section 9.1 of this is essentially the derivation you're looking for. | |
| Jan 13, 2023 at 18:41 | comment | added | Marcellus | Thank you. I'll look for that book right away. | |
| Jan 13, 2023 at 15:09 | comment | added | Cosmas Zachos | Merzbacher, like lots of authors (including me), leaves tedious plugin endurance marathon issues as "Exercises", often not worth the effort, clearly not his. Quite possibly, Goldberger & Watson's classic "Collisin Theory" book, the mother of all such "summaries" has more detail. As a parting hint, I would strongly urge you to read said chapter of the "Modern Quantum Mechanics" book by Sakurai & Napolitano, a masterpiece. I wish I had it available to me when learning. You can get free copies of it on the web, well-well worth opting for that chapter in lieu of Merzbacher. | |
| Jan 13, 2023 at 14:48 | comment | added | Marcellus | I am trying to learn this material on my own. I'm not in a class and have been making good progress, but this particular derivation eludes me. In this situation whether the derivation is an exercise or not shouldn't matter. The derivation requires something that I'm not seeing. I suspect the required insight is fairly simple, but then most things are simple when you see them! I appreciate your time and won't ask for more of it. | |
| Jan 13, 2023 at 12:11 | comment | added | Cosmas Zachos | Indeed, you have not been. It should be in your question that you are really asking for a solution manual answer to the subsequent Exercise 11.9 . The author left it as an exercise for a reason... | |
| Jan 13, 2023 at 5:25 | comment | added | Marcellus | Maybe I am not being clear. I can work through the procedure that Merzbacher and you described to get the desired equation. That is not difficult for me. However, in the middle of p. 244, Merzbacher states that the formula can also be obtained directly from the two equations I provided at the top of my post. I don't see how to use those two equations to get the formula. In other words, I haven't been able to use the alternate method that he mentions. I'd like to see that done. | |
| Jan 12, 2023 at 23:15 | comment | added | Cosmas Zachos | If you are unequivocally comfortable with eqn (11.82), you may derive (11.83) by using, as he stresses, the asymptotic forms (11.53), (10.26), and (10.30), which he took great (moving!) pains to establish in that and the previous chapter. But the book cannot be a substitute for a basic mathematical physics course. If you are conversant in orthogonal polynomials, asymptotic, and Green's functions, what he says is clear and solid. He is not Jackson's electrodynamics! | |
| Jan 12, 2023 at 22:31 | comment | added | Marcellus | I didn't mean to offend, I just would like someone to derive the equation that I mentioned. | |
| Jan 12, 2023 at 22:02 | comment | added | Cosmas Zachos | I can't read the book with you. If you have something less open-ended to be explained, fine, if you had specific limited questions, fine. But I cannot blindly rewrite/paraphrase 15 pages of something I last read in 1972, hoping it has enough detail to your satisfaction. | |
| Jan 12, 2023 at 20:48 | comment | added | Marcellus | I have Landau & Lifshitz and found on p. 517 a derivation that gives a similar result with the Born approximation. Thank you for that reference. However, I'd like to use the approach which, as you say, Merzbacher adumbrates but doesn't explicitly state. I suppose the derivation is trivial, but I just don't see it. I don't have Sakurai & Naplitano. Could you derive the equation for me? | |
| Jan 12, 2023 at 20:38 | comment | added | Cosmas Zachos | Sakurai & Naplitano, Ch 6, are slightly more explicit; but, frankly, Merzbacher adumbrates any and all glossed-over steps. | |
| Jan 12, 2023 at 20:28 | comment | added | Cosmas Zachos | But the text does derive it, no? You want a simpler text? Landau & Lifshitz, Ch XVII are quite informative.... | |
| Jan 12, 2023 at 20:14 | history | edited | Cosmas Zachos | CC BY-SA 4.0 |
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| Jan 12, 2023 at 18:52 | comment | added | Ghoster | Does this answer help? Does Wikipedia help? | |
| S Jan 12, 2023 at 18:09 | review | First questions | |||
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| S Jan 12, 2023 at 18:09 | history | asked | Marcellus | CC BY-SA 4.0 |