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A useful concept in Rydberg atoms is the notion of a channel. This concept is borrowed from scattering theory and describes all solutions of the Schrodinger equation for the scattering of the Rydberg electron of specified angular momentum with the ionic core in a certain energetic state. The bound Rydberg states correspond to scattering at negative energy ...

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The answer comes in several layers, as Martin has alluded to. I'll try and give a short summary: each point goes slightly deeper than the previous one. For an isolated atom, the labelling of the orbitals is arbitrary. That is to say, the $p_x$, $p_y$, and $p_z$ orbitals are all interchangeable. More formally, this reflects the isotropy of the system, which ...

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The very question you pose is addressed thoroughly in this open access work: https://www.nature.com/articles/ncomms9287 . The short answer to your question is that the electron density can be mapped using a technique akin to diffraction as described in their work. You mentioned a distinction between the electron density and the orbitals, and the orbital is ...

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J is the total angular momentum. L is the orbital angular momentum and S is the intrinsic total electron spin angular momentum. J = L + S L = $\sqrt{L\left(L+1\right)}\frac{h}{2\pi }$ --> L can be n-1 where n is the Principal quantum number S = $\sqrt{S\left(S+1\right)}\frac{h}{2\pi }$ --> S is an integer or half an odd integer, depending on whether ...

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A mechanical macroscopic counterpart, acoustical activity where mechanical transverse oscillation direction is being rotated, is described in Frenzel, T., Köpfler, J., Jung, E. et al. Ultrasound experiments on acoustical activity in chiral mechanical metamaterials. Nat Commun 10, 3384 (2019). The notion “activity” refers the rotation of the linear ...

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I asked this question way long back and with a lot more reading, I think I've come up with more specific points to answer this question. the most interesting part is that the wave orbitals are distinguishable (to some extent) but not the electrons ( particle itself) why is this? Every electron in a given atom is distinguishable in the sense that you will ...

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do states with different total angular momentum have necessarily different energies? Taking a diatomic rigid rotor model as an example the rotational energy is given by $$E_J = \frac{h^2 J(J+1)}{8\pi^2I}$$ so that if $J\ne J'$ the answer would obviously have to be $E_J \ne E_{J'}$ Each J state is degenerate with degeneracy $g_J=2J+1$. The total energy of ...

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In quantum chemistry numerical experimentation is the norm and rigorous mathematical proof the rare exception. As a result, not many rigorous results are know, not even for the good-old Hartree-Fock method. For a review of mathematical results I recommend you have a look at these references: Claude Le Bris, Computational chemistry from the perspective of ...

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