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=== Approximatio [[Maximus Born|Bornis]]-Oppenheimeris<ref>[https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation]</ref>===
Comparando energias kineticas nucleorum et electronum notamus massam levissimi [[Nucleus atomi|nuclei]] - hic [[Hydrogenium|hydrogenii]] ca. 2000-ies gravior esse electrono. Ergo energia kinetica nucleorum <math>T_n</math> magno minor est quam energia kinetica electronum <math>T_e</math> ita ut illa neglecta esse possit. Ita familiam Hamiltonianōrum electronicōrum habemus <math display="block">H_e=T_e+V_{nn}+V_{ne}+V_{ee}</math>cujus membra copiā locōrum nucleōrum <math display="inline">\{{\bf R}_{\alpha}|\alpha = 1,\ldots,A\}</math> distinguuntur. Physice, autem, quaeque data configuratio nucleōrum <math display="inline">\{{\bf R}_{\alpha}|\alpha = 1,\ldots,A\}</math> inducit campum vel potential electricum in quō electrones moventur; nuclei autem, quia ipsōrum energia kinetica zeri aequalis posita est, ''[[Mechanica Newtoniana|in statu suo quiescendi persĕvērant]].'' Motūs electronum in suo ordine functione undali solo electronum <math display="inline">\Psi_e(\mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_N) </math>, eandem functio undalis electronica nōmĭnēmus, exprĭmuntur. Quoniam Hamiltonianum electronicum pro quōque configuratione nucleōrum <math display="inline">\{{\bf R}_{\alpha}\}</math> potentialem electricam congruentem habet, functio undalis electronica aequationis Schödingeris staticae sătisfăciens aeque ab configuratione <math display="inline">\{{\bf R}_{\alpha}\}</math> pendet; ergo scribere possumus <math>\Psi_e=\Psi_e(\{\mathbf{x}_j\}\mid\{{\bf R}_{\alpha}\}) </math> ad dependentiam functionis electronicae ab configuratione <math>\{{\bf R}_{\alpha}\} </math> denotandum. Enimvero energia tota electronica quid est [[valor medius exspectatus]] Hamiltoniani electronici <math>E_e=\langle \Psi_e | H_e| \Psi_e \rangle_{\mathbf x}</math><ref>Hic subscriptum <math>{\mathrm x}</math> significat integrationem solo respectu variabilium electronicarum valorem medium calculando.</ref> est autem finctio configurationis <math>E_e=E_e(\{{\bf R}_{\alpha}\} ) </math> exprimens energiam potentialem,
=== Structura atomi ===
Atomi sunt systemata simplicissima ex electronibus ac nucleis compositae quia quaeque atomus solum nucleum habet/continet. Structura atomi modō [[Mechanica quantica|mechanicae quanticae]] describeri postest.
==== Atomus Hydrogenii ====
Ponendo nucleum requiscere, aequationem Schrödingeri pro atomō simplicissimā - illā hydrogenii, sed cum onere nuclei <math>Z</math> (numerō positivō integrō) scribere possumus:
<math display="block">\hat H \psi(\mathbf r) = \bigl(-\frac{\hbar^2\nabla^2}{2 m_{\mathrm e}} - \frac{Z{\mathrm e}^2}{\left \vert\mathbf r \right\vert}\bigr)\psi(\mathbf r) = E \psi(\mathbf r)</math>
quid in unitatibus atomicis trascribi potest <math display="block">\hat H \psi(\mathbf r) = \bigl(-\frac{\nabla^2}{2 } - \frac{Z}{\left \vert\mathbf r \right\vert}\bigr)\psi(\mathbf r) = E \psi(\mathbf r).</math>Ut eam [[Usor:Tchougreeff/QUOMODO sive HOW To/PRINCIPIA CALCULI DIFFERENTIALIS ET INTEGRALIS ITEMQUE CALCULI DIFFERENTIARUM FINITARUM AUCTORE ANDREA CARAFFA E SOCIETATE IESU ROMAE TYPIS IOANNIS BAPTISTAE MARINI ET SOCII MDCCCXLV#resolvere|resolvāmus]] a coordinatis [[Renatus Cartesius|cartesianis]] ad coordinatas sphaericas <math display="block">\mathbf r = (x,y,z) = r (\sin\theta\cos\varphi,\sin\theta\sin\varphi,\cos \theta) </math>transeāmus, in quibus operator Laplacianus in coordinatis cartesianis formam: <math display="block">\nabla^2 = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} </math> habens, accipit autem formam
==== Atomi cum pluribus electronibus ====
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