scholarly journals The Morbid Equation of Quantum Numbers

2021 ◽  
Author(s):  
XD Dongfang
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Bound States ◽  
Valence Electron ◽  
Coulomb Field ◽  
Bound State ◽  
Quantum Model ◽  
Conservation Of Energy ◽  
Quantum Numbers ◽  
The Law

The quantum model of valence electron generation orbital penetration of alkali metal elements with unique stable structure is investigated. The electric field outside the atomic kernel is usually expressed by the Coulomb field of the point charge mode, and the composite electric field in atomic kernel can be equivalent to the electric field inside the sphere with uniform charge distribution or other electric fields without divergence point. The exact solutions of two Schrödinger equations for the bound state of the Coulomb field outside the atom and the binding state of the equivalent field inside the atom determine two different quantization energy formulas respectively. Here we show that the atomic kernel surface is the only common zero potential surface that can be selected. When the orbital penetration occurs, the law of conservation of energy requires that the energy level formulas of the two bound states must have corresponding quantum numbers to make them equal. As a result, there is no solution to the quantum number equation, indicating that the two quantum states of the valence electron are incompatible. This irreconcilable contradiction shows that the quantized energy of quantum mechanics cannot absolutely satisfy the law of conservation of energy.

scholarly journals The Morbid Equation of Quantum Numbers

2020 ◽  
Author(s):  
XD Dongfang
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Valence Electron ◽  
Coulomb Field ◽  
Bound State ◽  
Quantum Model ◽  
Conservation Of Energy ◽  
Divergence Point ◽  
Quantum Numbers ◽  
The Law

The quantum model of valence electron generation orbital penetration of alkali metal elements with unique stable structure is investigated. The electric field outside the atomic kernel is usually expressed by the Coulomb field of the point charge mode, and the composite electric field in atomic kernel can be equivalent to the electric field inside the sphere with uniform charge distribution or other electric fields without divergence point. The exact solutions of two Schrödinger equations for the bound state of the Coulomb field outside the atom and the binding state of the equivalent field inside the atom determine two different quantization energy formulas respectively. Here we show that the atomic kernel surface is the only common zero potential surface that can be selected. When the orbital penetration occurs, the law of conservation of energy requires that the two energy level formulas must have corresponding quantum numbers to make them equal. As a result, there is no solution to the quantum number equation, indicating that the two quantum states of the valence electron are incompatible. This irreconcilable contradiction shows that the quantized energy of quantum mechanics cannot absolutely satisfy the law of conservation of energy.

scholarly journals Comment on: “Some quantum aspects of a particle with electric quadrupole moment interacting with an electric field subject to confining potentials”

2020 ◽  
Vol 35 (25) ◽  
pp. 2075002
Author(s):  
Francisco M. Fernández
Keyword(s):  
Electric Field ◽  
Quadrupole Moment ◽  
Bound States ◽  
Electric Quadrupole ◽  
Bound State ◽  
Electric Quadrupole Moment ◽  
Bound State Spectrum ◽  
Moving Particle ◽  
Quantum Aspects

We analyze the results obtained from a model consisting of the interaction between the electric quadrupole moment of a moving particle and an electric field. We argue that the system does not support bound states because the motion along the [Formula: see text] axis is unbounded. It is shown that the author obtains a wrong bound-state spectrum for the motion in the [Formula: see text] plane and that the existence of allowed cyclotron frequencies is an artifact of the approach.

scholarly journals Dynamic Role of the Correlation Effect Revealed in the Exceptionally Slow Autodetachment Rates of the Vibrational Feshbach Resonances in the Dipole-Bound State

2021 ◽  
Author(s):  
Do Hyung Kang ◽  
Jinwoo Kim ◽  
Sang Kyu Kim
Keyword(s):  
Real Time ◽  
Bound States ◽  
Valence Electron ◽  
Dynamic Range ◽  
Golden Rule ◽  
Bound State ◽  
Correlation Effect ◽  
The State ◽  
Feshbach Resonances ◽  
Halogenated Compound

Real-time autodetachment dynamics of the loosely-bound excess electron from the vibrational Feshbach resonances of the dipole-bound states (DBS) of 4-bromophonoxide (4-BrPhO-) and 4-chlorophenoxide (4-ClPhO-) anions have been thoroughly investigated. The state-specific autodetachment rate measurements obtained by the picosecond time-resolved pump-probe method on the cryogenically cooled anions, exhibit the exceptionally long lifetime (τ) of ~ 2.5  0.6 ns (as the upper bound) for the 11’1 vibrational mode of the 4-BrPhO- DBS. Strong mode-dependency in the wide dynamic range has also been found, giving τ ~ 5.3 ps for the 10’1 mode, for instance. Though it is nontrivial to get the state-specific rates for the 4-ClPhO- DBS, the average autodetachment lifetime of the 19’120’1/11’1 mode has been estimated to be ~ 548  108 ps. Observation of these exceptionally slow autodetachment rates of vibrational Feshbach resonances strongly indicates that the ‘correlation effect’ may play a significant role in the DBS photodetachment dynamics. The Fermi’s golden rule has been invoked so that the correlation effect is taken into account in the form of the interaction between the charge and the induced dipole where the latter is given by the polarizable counterparts of the electron-rich halogenated compound and the diffuse non-valence electron. This report suggests that one may measure, from the real-time autodetachment dynamics, the extent of the correlation effect contribution to the stabilization and/or dynamics of the excess non-valence electron among many different types of the long-range interactions of the DBS.

scholarly journals Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

2018 ◽  
Vol 855 ◽  
pp. 210-235 ◽  
Author(s):  
M. G. Blyth ◽  
D. Tseluiko ◽  
T.-S. Lin ◽  
S. Kalliadasis
Keyword(s):  
Electric Field ◽  
Bound States ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Film Surface ◽  
Wave Model ◽  
Bound State ◽  
Long Wave ◽  
Finite Set ◽  
Solitary Pulse

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.

scholarly journals IS QFT WITH EXTERNAL BACKGROUNDS A CONSISTENT MODEL?

2011 ◽  
Vol 03 ◽  
pp. 58-64
Author(s):  
S. P. GAVRILOV ◽  
D. M. GITMAN
Keyword(s):  
Dirac Equation ◽  
Electric Field ◽  
Electric Fields ◽  
Strong Electric Field ◽  
Coulomb Field ◽  
Back Reaction ◽  
Consistent Model

We discuss consistency of the concept of external background in QFT. Different restrictions on magnitude of magnetic and electric fields are analyzed. The back reaction due to strong electric field is calculated and restrictions on the magnitude and duration of such a field are obtained. The problem of consistency of Dirac equation with a superstrong Coulomb field is discussed.

Aharonov–Bohm effect in a Coulomb-type potential under the influence of a cutoff point

2021 ◽  
pp. 2150136
Author(s):  
K. Bakke
Keyword(s):  
Electric Fields ◽  
Bound States ◽  
Energy Levels ◽  
Bound State ◽  
Cutoff Point ◽  
Coulomb Type ◽  
Bohm Effect ◽  
Forbidden Region ◽  
Aharonov Bohm ◽  
Type Potential

We analyze the influence of a cutoff point on a Coulomb-type potential that stems from the interaction of an electron with electric fields. This cutoff point establishes a forbidden region for the electron. Then, we search for bound state solutions to the Schrödinger equation. In addition, we consider a rotating reference frame. We show that the effects of rotation break the degeneracy of the energy levels. Further, we discuss the Aharonov–Bohm effect for bound states.

scholarly journals A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

2016 ◽  
Vol 10 ◽  
pp. 8-22
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Star Product ◽  
Three Dimensional ◽  
Spin Symmetry ◽  
Hamiltonian Operator ◽  
Bound State ◽  
Exact Bound ◽  
Quantum Numbers ◽  
Quantum Symmetries

New exact bound state solutions of the deformed radial upper and lower components of Dirac equation and corresponding Hermitian anisotropic Hamiltonian operator are studied for the modified Kratzer-Fues potential (m.k.f.) potential by using Bopp’s shift method instead to solving deformed Dirac equation with star product. The corrections of energy eigenvalues are obtained by applying standard perturbation theory for interactions in one-electron atoms. Moreover, the obtained corrections of energies are depended on two infinitesimal parameters (θ,χ), which induced by position-position noncommutativity, in addition to the discreet nonrelativistic atomic quantum numbers: (j=l±1/1,s=±1/2,landm) and we have also shown that, the usual relativistic states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended quantum symmetries (NC: 3D-RS).

Expectation Values of Quasibound States: Nuclear Quadrupole Coupling Constants of BH in the X1 Σ+ and B1 Σ+ States

1998 ◽  
Vol 63 (9) ◽  
pp. 1309-1320
Author(s):  
Michal Juřek ◽  
Vladimír Špirko ◽  
Wolfgang P. Kraemer
Keyword(s):  
Bound States ◽  
Bound State ◽  
Coupling Constants ◽  
Electric Field Gradients ◽  
Expectation Values ◽  
Field Gradients ◽  
Quantum Numbers ◽  
Quadrupole Coupling ◽  
Vibrational Levels ◽  
Nuclear Quadrupole

The 10B and 11B nuclear quadrupole coupling constants of the bound and quasibound rotation-vibrational levels of BH in the ground X~1Σ+ and double-minimum excited B~1Σ+ electronic states are evaluated using ab initio calculated potentials and electric field gradients. The predicted expectation values of the resonance states are found to be smooth continuations of those of the bound states, but their dependence on the rotational and vibrational quantum numbers differs from the standard Dunham-type polynomial dependences obtained for bound state constants.

IS QFT WITH EXTERNAL BACKGROUNDS A CONSISTENT MODEL?

2011 ◽  
Vol 26 (22) ◽  
pp. 3752-3758 ◽  
Author(s):  
S. P. GAVRILOV ◽  
D. M. GITMAN
Keyword(s):  
Dirac Equation ◽  
Electric Field ◽  
Electric Fields ◽  
Strong Electric Field ◽  
Coulomb Field ◽  
Back Reaction ◽  
Consistent Model

We discuss consistency of the concept of external background in QFT. Different restrictions on magnitude of magnetic and electric fields are analyzed. The back reaction due to strong electric field is calculated and restrictions on the magnitude and duration of such a field are obtained. The problem of consistency of Dirac equation with a superstrong Coulomb field is discussed.

Density matrices for atoms and solids. I. Effective potential matrix and the Bloch equation

1967 ◽  
Vol 300 (1462) ◽  
pp. 391-404 ◽  
Keyword(s):  
Density Matrix ◽  
Effective Potential ◽  
Bound States ◽  
Analytic Solution ◽  
Iterative Scheme ◽  
Coulomb Field ◽  
Bound State ◽  
Bloch Equation ◽  
Approximate Analytic Solution ◽  
Potential Matrix

By recognizing that the canonical density matrix C can be expressed in terms of an effective potential matrix, U , intimately related to the potential V in which the particles move, a powerful approximate analytic solution of the Bloch equation has been obtained. This solution for U reduces ( a ) to first-order perturbation theory on C when V is weak and ( b ) to the correct Thomas–Fermi result when V is almost constant in space. For an attractive defect centre in a metal, represented by a screened Coulomb potential which is not strong enough to bind an electron, it is shown that this approximate analytic solution may be used successfully in a numerical iterative solution of the Bloch equation and final numerical results are presented. For more strongly attractive centres, however, where bound states appear, the same numerical iterative scheme proves inadequate. A method is developed which orthogonalizes the approximate analytical density matrix to the wave function product for the lowest bound state. The new density matrix thereby formed is tested, and found to work successfully for an unscreened Coulomb field. This approach is then worked out for a screened potential created by a charge Z = 4 in a Fermi gas of density equal to that in Cu metal. Such a charged centre brings down a bound state from the conduction band and it is shown that the method employed successfully for the bare Coulomb field also leads to an accurate solution of the Bloch equation in this case. It is concluded that we have here a sufficiently powerful iterative scheme to carry out Hartree self-consistent calculations based on the Dirac density matrix, both for atoms, where the Fermi level lies in the bound state region, and for defects in metals, where the Fermi energy falls in the continuum. Such calculations are now in progress.

Sign in / Sign up

Export Citation Format

Share Document