Related papers: Still learning about space dimensionality: from the description of hydrogen atom by a generalized wave equation for dimensions D$\geq$3

Still learning about space dimensionality: from the description of hydrogen atom by a generalized wave equation for dimensions D$\geq$3

URL: http://arxiv.org/abs/2009.13473v2
Date: Mon, 7 Nov 2022 16:49:30 GMT
Title: Still learning about space dimensionality: from the description of hydrogen atom by a generalized wave equation for dimensions D$\geq$3
Authors: Francisco Caruso, Vitor Oguri, Felipe Silveira
Abstract summary: It is shown that new light can be shed on the problem of understanding the dimensionality of the world. For the first time, we can understand that not only the sign of energy but also the value of the ground state energy of hydrogen atom is related to the threefold nature of space.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The hydrogen atom is supposed to be described by a generalization of Schr\"{o}dinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. Starting from previously obtained solutions for this equation using the $1/N$ expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul Ehrenfest. A surprisingly new result is obtained. Indeed, for the first time, we can understand that not only the sign of energy but also the value of the ground state energy of hydrogen atom is related to the threefold nature of space.

Related papers

Energetics of the dissipative quantum oscillator [22.76327908349951]
We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy. We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
arXiv Detail & Related papers (2023-10-05T15:18:56Z)
Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
arXiv Detail & Related papers (2023-06-21T10:11:28Z)
Arbitrary $\ell$-state solutions of the Klein-Gordon equation with the Eckart plus a class of Yukawa potential and its non-relativistic thermal properties [0.0]
We present any $ell$-state energy eigenvalues and the corresponding normalized wave functions of a mentioned system in a closed form. We calculate the non-relativistic thermodynamic quantities for the potential model in question, and investigate them for a few diatomic molecules.
arXiv Detail & Related papers (2023-04-01T23:22:23Z)
The three-body scattering hypervolume of identical fermions in one dimension [8.35070936044077]
We study the zero-energy collision of three identical spin-polarized fermions with short-range interactions in one dimension. We derive the expansions of the three-body wave function when the three fermions are far apart or one pair and the third fermion are far apart. We calculate the shifts of energy and of pressure of spin-polarized one-dimensional Fermi gases due to a nonzero $D_F$ and the three-body recombination rate in one dimension.
arXiv Detail & Related papers (2023-02-27T11:43:03Z)
Analytic study of conformable Schrodinger equation with Hydrogen atom [0.0]
Conformable Schrodinger equation for hydrogen atom with given conformable potential is solved. Traditional energy levels and wave function for hydrogen atom are recovered when $alpha = 1$.
arXiv Detail & Related papers (2022-09-05T16:12:32Z)
The Origin of the Born Rule from Spacetime Averaging [0.0]
We consider a particle in a one-dimensional square well potential in a superposition of two states and average the energy over space and time. We show that, for most cases, such an energy expectation value differs by only a few percent from that calculated using the Born rule. This difference is consistent with experimental tests of the expectation value and suggests that the Born rule may be an approximation of spacetime averaging.
arXiv Detail & Related papers (2021-10-12T23:02:11Z)
The hydrogen atom: consideration of the electron self-field [0.0]
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen. We demonstrate that only particular classes of solutions, "nonlinear" analogues of s- and p-states, can be obtained through decomposition of a solution in a series.
arXiv Detail & Related papers (2021-01-05T21:52:41Z)
$\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
arXiv Detail & Related papers (2020-12-15T17:08:33Z)
Anharmonic oscillator: a solution [77.34726150561087]
The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
arXiv Detail & Related papers (2020-11-29T22:13:08Z)
On the four-body problem in the Born-Oppenheimer approximation [0.0]
The model allows exact solvability and a critical analysis of the Born-Oppenheimer approximation. It is shown that the sum of the first two terms of the Puiseux series, in powers of the dimensionless parameter $sigma=fracmM$, coincide exactly with the values obtained in the Born-Oppenheimer approximation.
arXiv Detail & Related papers (2020-07-29T16:43:03Z)
Probing spin correlations in a Bose-Einstein condensate near the single atom level [26.500149465292246]
We produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. A novel fluorescence imaging technique with sensitivity $Delta N sim 1.6$ atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics.
arXiv Detail & Related papers (2020-04-20T00:50:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.