{"id":292,"date":"2018-04-23T07:44:14","date_gmt":"2018-04-23T07:44:14","guid":{"rendered":"http:\/\/www.milq.info\/?page_id=292"},"modified":"2026-08-05T18:12:52","modified_gmt":"2026-08-05T16:12:52","slug":"m45_zur_aufenthaltswahrscheinlichkeit","status":"publish","type":"page","link":"https:\/\/www.milq.info\/en\/m45_zur_aufenthaltswahrscheinlichkeit\/","title":{"rendered":"On the Probability Density"},"content":{"rendered":"
<\/div>

<\/p>\n

On the probability density in antiprotonic hydrogen<\/h3>\n

Experiments on electron-positron annihilation at the PETRA storage ring at DESY have shown that the size of an electron is at least a factor of 1,000 smaller than that of a proton, yet an electron cloud in the hydrogen atom is 40,000 times larger than a proton.<\/p>\n

Slow antiprotons (the negatively charged antiparticles of protons) can be captured by atomic nuclei. The nucleus together with the bound antiproton is referred to as an antiprotonic atom<\/strong>. Because of its mass, the antiproton is located much closer to the nucleus than the remaining shell electrons, so that their influence can largely be neglected. The antiprotons are captured in high quantum states, and the transitions can be observed via photon emission in the keV range. In antiprotonic hydrogen, the transition from the \"2p\" state to the \"1s\" state can be observed. In contrast to ordinary hydrogen, this line is very broad. Because of Heisenberg’s uncertainty relation, this points to a short lifetime.<\/p>\n

Precisely in the ground state \"n = 1\", the proton and the antiproton come so close to each other that they can annihilate. This produces several \"\pi\" mesons. This is understandable within the Schr\u00f6dinger picture, since the \"1s\" wave function has its maximum at a distance of \"r = 0\"; that is, the proton and the antiproton have their highest probability density there.<\/p>\n

In the Bohr model, by contrast, the two particles orbit their common center of mass and are separated by a distance greater than the range of the strong interaction. Annihilation is therefore not possible. The experimental finding described above cannot be reconciled with the Bohr model of the atom. This is a further argument against the Bohr model.<\/p>\n

For more information, see the article by P. Schm\u00fcser in “Praxis der Naturwissenschaften” 8\/48, 1999, p. 11ff.<\/p>\n

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On the probability density in antiprotonic hydrogen Experiments on electron-positron annihilation at the PETRA storage ring at DESY have shown that the size of an electron is at least a factor of 1,000 smaller than that of a proton, yet an electron cloud in the hydrogen atom is 40,000 times larger than a proton. Slow… Continue reading On the Probability Density<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-292","page","type-page","status-publish","hentry","without-featured-image"],"yoast_head":"\nOn the Probability Density - milq<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.milq.info\/en\/m45_zur_aufenthaltswahrscheinlichkeit\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"On the Probability Density - milq\" \/>\n<meta property=\"og:description\" content=\"On the probability density in antiprotonic hydrogen Experiments on electron-positron annihilation at the PETRA storage ring at DESY have shown that the size of an electron is at least a factor of 1,000 smaller than that of a proton, yet an electron cloud in the hydrogen atom is 40,000 times larger than a proton. 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