Dear Sam, Thank you for your contribution; once I saw a figure in which the plane wave continues into the MT region but enlarged, which confused me.
________________________________ De: Wien <[email protected]> en nombre de Sam Trickey <[email protected]> Enviado: viernes, 22 de marzo de 2019 08:13 a. m. Para: [email protected] Asunto: Re: [Wien] Augmented Plane Wave Rarely do I contribute to this list, though I benefit from reading it. I must respectfully contradict Martin. Professor Slater clearly intended that the augmentation be of the plane wave. The history, at least as I know it, is this. Professor Slater did not use the word "augment" or "augmented" in his 1937 paper that usually is cited as the original APW paper [Rev. 51, 846 (1937)]. So far as I am aware, the first time he used the phrase "augmented plane wave" is in Phys. Rev. 92, 603 (1953). The phrase appears in the title but, more important for discerning his intent is the discussion beginning on the bottom right of p. 603 and continuing on 604. He introduces Herring's orthogonalized plane waves and summarizes their applications and then says (lines 7-9, LH column, p. 604) "Relatively few such orthogonalized or augmented plane waves suffice to give a rather good approximate wave function." Noting the problem of non-existent orthogonalization of a 2p-like state to a deeper core state found by Frank Herman, Prof. Slater goes on to say "Herman has suggested that in such a case we could augment the plane wave ...". He opens the next paragraph with "The present method may be regarded as a straight-forward procedure for augmenting a plane wave by adding to it a contribution near each nucleus ...". It may be useful to add that I was part of Prof. Slater's group within QTP for the last 7-1/2 years of his life and one year was assigned (even though I was an Asst. Prof. not a post-doc!) to be his teaching assistant in his "Quantum Theory of Matter" course. Those experiences were consistent with the sentences just quoted. Peace, Sam On 3/22/19 7:04 AM, pieper wrote: Dear Pablo, I suspect your problem occurs because you left out the word which "Augmented" refers too: It is an "Augmented Plane Wave Method", that is, the Method is augmented (including additional basis functions), not the plane waves (in amplitude or intensity). Best regards, Martin Pieper --- Dr. Martin Pieper Karl-Franzens University Institute of Physics Universitätsplatz 5 A-8010 Graz Austria Tel.: +43-(0)316-380-8564 Am 2019-03-22 02:49, schrieb delamora: Dear Wien users, I have a question about the name of "Augmented Plane Wave" I had the idea that when the wave enters the Muffin Tin sphere the amplitude of the wave increased. Trying to see this I found that when a wave crosses a step function, https://urldefense.proofpoint.com/v2/url?u=https-3A__quantummechanics.ucsd.edu_ph130a_130-5Fnotes_node149.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=CV5sXDCtZrDlO2GFM8sW4hec5wD0wT0O34PcltW3ZfI&e= When the incoming wave exp(ikx) reaches an upwards step function there is a reflected wave R exp(-ikx) and a transmitted wave T exp(ik'x) what this article shows is; 1 + R = T That is, the amplitudes of the incoming wave and the reflected wave add to the amplitude of the transmitted wave If I take this into a square well then I would understand that the waves inside the well have the total amplitude equal to the incoming and transmitted wave. That is, when the wave enters the Muffin Tin the amplitude of wave is not AUGMENTED. So why is this method called "Augmented Plane Wave"? Saludos Pablo _______________________________________________ Wien mailing list [email protected]<mailto:[email protected]> https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=QELHbpUlFIYdizaiEh0uSI_fcbgFXMcKs25dMRPSkU0&e= SEARCH the MAILING-LIST at: https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=p2zeCI2PUnzFXnYuR6JhoHGW3GZi1dVfbW6410meyh4&e= _______________________________________________ Wien mailing list [email protected]<mailto:[email protected]> https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=QELHbpUlFIYdizaiEh0uSI_fcbgFXMcKs25dMRPSkU0&e= SEARCH the MAILING-LIST at: https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=p2zeCI2PUnzFXnYuR6JhoHGW3GZi1dVfbW6410meyh4&e= -- Samuel B. Trickey QTP, Depts. of Physics and Chemistry 2324 Physics Building Box 118435 Univ. of Florida Gainesville, FL 32611-8435 Vox: 352-392-6978 (direct) Vox: 352-392-1597 (receptionist) Fax: 352-392-8722 http://www.qtp.ufl.edu/ofdft http://users.clas.ufl.edu/trickey
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