{"id":2843,"date":"2026-07-23T08:47:41","date_gmt":"2026-07-23T06:47:41","guid":{"rendered":"https:\/\/www.milq.info\/m55_n-abhaengigkeit_der_energiewerte\/"},"modified":"2026-07-23T08:47:41","modified_gmt":"2026-07-23T06:47:41","slug":"m55_n-abhaengigkeit_der_energiewerte","status":"publish","type":"page","link":"https:\/\/www.milq.info\/en\/m55_n-abhaengigkeit_der_energiewerte\/","title":{"rendered":"n-dependence of the energy values"},"content":{"rendered":"
<\/div>

The method in which the Coulomb potential is replaced by a suitably adapted box potential yields the correct \"n\"-dependence of the hydrogen energy values: \"E_{ges} \sim -1/n^2\".<\/p>\n

This raises a question: the energy values of an (ordinary) potential well are proportional to \"n^2\" (cf. Equation \"(2)\" in the main text). How, then, can a potential-well model yield an energy dependence of \"1/n^2\"?<\/p>\n

Answer: the parameters of the potential well (\"R\" and \"W_0\") themselves contain the energy \"E_{ges}\" (cf. Equation \"(1)\" in the main text). If these energy-dependent parameters are substituted into the energy formula \"(2)\", \"E_{ges}\" appears on both sides of the equation. Solving the equation for \"E_{ges}\" can then yield a different \"n\"-dependence than the original \"E \sim n^2\" \u2014 and this is exactly what happens here.<\/p>\n

This aspect of the method presented is somewhat difficult to see through: in essence, a different potential well is fitted to each value of \"E_{ges}\".<\/p>\n

Back to the chapter overview<\/a>.<\/p>","protected":false},"excerpt":{"rendered":"

The method in which the Coulomb potential is replaced by a suitably adapted box potential yields the correct -dependence of the hydrogen energy values: . This raises a question: the energy values of an (ordinary) potential well are proportional to (cf. Equation in the main text). How, then, can a potential-well model yield an energy… Continue reading n-dependence of the energy values<\/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-2843","page","type-page","status-publish","hentry","without-featured-image"],"yoast_head":"\nn-dependence of the energy values - 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\/m55_n-abhaengigkeit_der_energiewerte\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"n-dependence of the energy values - milq\" \/>\n<meta property=\"og:description\" content=\"The method in which the Coulomb potential is replaced by a suitably adapted box potential yields the correct -dependence of the hydrogen energy values: . 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This raises a question: the energy values of an (ordinary) potential well are proportional to (cf. Equation in the main text). 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