Figure 3 - uploaded by Jixuan Hou
Content may be subject to copyright.
Context in source publication
Context 1
... on the previous analysis on the hydrogen molecules, our simplification here does not affect calculating the bond length and ground state energy of hydridohelium. Then, the Eq. (6) can be rewritten as The diagram of bonded helium hydride ion is shown in Fig. 3. r 1 and r 2 are the reduced distances from electrons to the hydrogen nucleus and to the helium nucleus, respectively. x is the reduced distance from the plane of the bonded two electrons to the hydrogen nucleus, 0 < x < l. Each electron is still subjected by three Coulomb forces. In the horizontal direction, there is along the ...
Similar publications
The London dispersion interactions between systems undergoing bond breaking, twisting, or compression are not well studied due to the scarcity and the high computational cost of methods being able to describe both the dynamic correlation and the multireference character of the system. Recently developed methods based on the Generalized Valence Bond...
A least information principle is proposed here to derive the formulations of non-relativistic quantum mechanics, including the uncertainty relation and the Schr\"{o}dinger equation in both position and momentum representations. The key element for this principle is the introduction of new metrics to measure the observable information due to vacuum...
In this paper, a non-trivial system governed by a continuum PT-symmetric Hamiltonian is discussed. We show that this Hamiltonian is iso-spectral to the simple harmonic oscillator. We find its eigenfunctions and the path in the complex plane along which these functions form an orthonormal set. We also find the hidden symmetry operator, [Formula: see...
Boxworld is a theory in which any no-signalling distribution can be realised. It hence has more nonlocality than quantum theory, enhancing certain information processing tasks. However, this richness in correlations necessarily leads to a poorer set of possible measurements -- it is known for example that there is no analogue of a Bell basis measur...
This is a dialogue between Huw Price and Travis Norsen, loosely inspired by a letter that Price received from J. S. Bell in 1988. The main topic of discussion is Bell's views about retrocausal approaches to quantum theory, and their relevance to contemporary issues.
Citations
... While the semiclassical Bohr model of the atom is lacking in the very fundamental sense that it predicts non-spherical atoms (the atoms, or at the very least the hydrogen atom and single-electron ions, are flat discs), it is still "correct enough" to predict chemical bonding, as has been shown under different assumptions both with pedagogical [1,2,3] and more technical aims [4,5] and already by Bohr himself who predicted a stable H 2 molecule with a very reasonable binding energy [6,7]. In hindsight, one problem with Bohr's approach is that the circular orbits, even in the isolated atom, correspond to a state of unphysically high angular momentum. ...
With a pedagogical aim suited for the upper-division undergraduate, we apply the old quantum theory (pre-Schrödinger) to the study of many-electron atomic species. We eschew the typical picture with circular atomic Bohr orbits of non-zero angular momentum and instead consider the electrons to be 'bouncing' along straight lines on the nucleus. Abandoning the circular orbits of Bohr comes at the cost of a meanfield approximation but at the gain of a physically correct (vanishing) electron angular momentum for the first four elements. The Bohr–Sommerfeld meanfield (or perturbation) calculations, of which we present a variety of increasing numerical complexity, generally give results accurate to within a few percent. For He, also excited states are calculated and these results quickly converge on the exact values already for the first excited state. The main source of error in the semiclassical calculation with respect to the exact results is traced to the neglect of the Pauli principle, since it is virtually present only for the singlet ground-state but not the lowest triplet state.
