Extension of the Gradient Effect on Eigenenergies to the “Electric Stern-Gerlach” Effect With Square of theLinearized Field

J.D.  Bulnes; M.A.I.  Travassos; D.A.  Juraev; J.L.  López-Bonilla

doi:10.22105/kmisj.v1i2.64

Authors

J.D. Bulnes Department of Exact and Technological Sciences, Federal University of Amapá, Rod. J. Ku- bitschek, 68903-419, Macapá, AP, Brazil.
M.A.I. Travassos Department of Exact and Technological Sciences, Federal University of Amapá, Rod. J. Ku- bitschek, 68903-419, Macapá, AP, Brazil.
D.A. Juraev Scientific Research Center, Baku Engineering University, Baku AZ0102, Azerbaijan.
J.L. López-Bonilla ESIME−Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, Mexico.

https://doi.org/10.22105/kmisj.v1i2.64

Downloads

Abstract

In this paper, we constructed a solution of the Schrödinger equation for the ammonia molecule, modeled as a particle with a permanent electric dipole moment, which can access only two quantum states, as part of a beam of these molecules entering a region where an electrostatic field with a weak gradient act. In this solution, the contribution of the electric field gradient to the eigenenergies of the molecule stands out in the context of linearization of the square of one of the components of the electrostatic field. This result indicates that the analogy established between the spatial separation of this beam of molecules and the spatial separation of silver atoms in the inhomogeneous magnetic field in the Stern-Gerlach effect is not limited only to spatial separation; the gradient effect on eigenenergies, recently identified in the Stern-Gerlach case, also manifests itself in the case of ammonia molecules in an inhomogeneous electrostatic field.

Keywords

Electric dipole moment Polarizability matrix Analogy with the Stern-Gerlach effect

References (30)

[1] J.D. Bulnes, M.A.I. Travassos, D.A. Juraev, J. López-Bonilla, From the Hamilton-Jacobi equation to the Schrödinger equation and vice versa, without additional terms and approximations, Himalayan Physics, 11, 21–27 (2024).

[2] J.D. Bulnes, M.A.I. Travassos, D.A. Juraev, G. Dias and J. López-Bonilla, Mathematical simulation of à la Einstein loss of the non-separable character of a function for two particles at the quantum-classical boundary, Open Journal of Mathematical Sciences, 8, 113–127 (2024).

[3] J.D. Bulnes, M.A.I. Travassos, D.A. Juraev, J.E. Ottoni, J. López-Bonilla, Stern-Gerlach Centennial: Parity, gradient effect, and an analogy with the Higgs field, Himalayan Physics, 11, 68–77 (2024).

[4] J.D. Bulnes, An unusual quantum entanglement consistent with Schrödinger’s equation, Global and Stochastic Analysis, 9, 79–87 (2022).

[5] J.D. Bulnes, M.A.I. Travassos, H.E. Caicedo-Ortiz, J. López-Bonilla, Más de un tipo de entrelazamiento en el mundo cuántico y ninguno en el mundo clásico, Journal de Ciencia e Ingeniería, 16:1, 5–12 (2024).

[6] J.D. Bulnes, D.A. Juraev, J.L. López-Bonilla, M.A.I. Travassos, Exact de coupling of a coupled system of two stationary Schrödinger equation, Stochastic Modelling Computational Sciences, 3, 23–28 (2023).

[7] J.D. Bulnes, J.L. López-Bonilla, D.A. Juraev, Klein-Gordon’s equation for magnons without non-ideal effect on spatial separation of spin waves, Stochastic Modelling and Computational Sciences, 3:1, 29–37 (2023).

[8] J.D. Bulnes, J.L. López-Bonilla, Dirac’s linearization applied to the functional, with matrix aspect, for the time of flight of light, Maltepe Journal of Mathematics, 4:2, 38–43 (2022).

[9] J.D. Bulnes, Solving the heat equation by solving an integro-differential equation, Global and Stochastic Analysis, 9:2, 89–97 (2022).

[10] J.D. Bulnes, F.A. Bonk, A case of spurious quantum entanglement originated by a mathematical property with a nonphysical parameter, Latin-American Journal of Physics Education, 8, 4306-1–4306-4 (2014).

[11] J.D. Bulnes, L.A. Peche, Entrelazamiento cuántico espúrio con matrizes seudopuras extendidas 4 por 4, Revista Mexicana de Física, 57, 188–192 (2011).

[12] J.D. Bulnes, Propagadores cuánticos calculados de acuerdo con el postulado de Feynman con caminos aproximados por polinomios, Revista Mexicana de Física, 55, 34–43 (2009).

[13] J.D. Bulnes, I.S. Oliveira, Construction of exact solutions for the Stern Gerlach effect, Brazilian Journal of Physics, 31:3, 488–495 (2001).

[14] D.A. Juraev, N.M. Mammadzada and M. Israr, On the Application of Ill-posed problems of equations of mathematical physics, Karshi Multidisciplinary International Scientific Journal, 1:2, 43–50 (2024).

[15] D.A. Juraev, P. Agarwal, A. Shokri, E.E. Elsayed, Integral formula for matrix factorizations of Helmholtz equation, Recent trends in fractional calculus and its applications, advanced studies in complex systems, Elsevier, pp. 123–146 (2024).

[16] D.A. Juraev, P. Agarwal, A. Shokri, E.E. Elsayed, Cauchy problem for matrix factorizations of Helmholtz equation on a plane, Recent trends in fractional calculus and its applications, advanced studies in complex systems, Elsevier, pp. 147–175 (2024).

[17] D.A. Juraev, P. Agarwal, A. Shokri, E.E. Elsayed, The Cauchy problem for matrix factorizations of Helmholtz equation in space, Recent trends in fractional calculus and its applications, advanced stud ies in complex systems, Elsevier, pp. 177–210 (2024).

[18] D.A. Juraev, Y.S. Gasimov, On the Regularization Cauchy Problem for Matrix Factorizations of the Helmholtz Equation in a Multidimensional Bounded Domain, Azerbaijan Journal of Mathematics, 2:1, 142 (2022).

[19] D.A. Juraev, Solution of the Ill-posed Cauchy problem for matrix factorizations of the Helmholtz equation on the plane, Global and Stochastic Analysis, 8:3, 1–17 (2021).

[20] D.A. Juraev, A.A. Tagiyeva, J.D. Bulnes and B. Drumea, On the regularization of the Cauchy problem for matrix factorizations of the Helmholtz equation in Rm, Karshi Multidisciplinary International Scientific Journal, 1:2, 51–68 (2024).

[21] D.A. Juraev, N.M. Mammadzada, J.D. Bulnes, S.K. Gupta, G.A. Aghayeva, V.R. Ibrahimov, Regularization of the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain, Mathematics and Systems Science, 2:2, 1–16 (2024).

[22] D.A. Juraev, A.A. Tagiyeva, J.D. Bulnes and G.X.-G. Yue, On the solution of the Ill-posed Cauchy problem for elliptic systems of the first order, Karshi Multidisciplinary International Scientific Journal, 1:1, 17–26 (2024).

[23] D.A. Juraev, P. Agarwal, A. Shokri, E.E. Elsayed, J.D. Bulnes, On the solution of the Ill-posed Cauchy problem for elliptic systems of the first order, Stochastic Modelling & Computational Sciences, 3, 1–21, (2023).

[24] R.P. Feynman, R. Leighton, M. Sands, Feynman Lectures on Physics, Vol. III, Addison-Wesley, Massachusetts (1965).

[25] C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics, Vol. I, Hermann and Wiley, Paris (1977).

[26] M. Alonso, E.J. Finn, Fundamental University Physics, Quantum and Statistical Physics, Vol. III, Addison-Wesley (1968).

[27] A. A. Vuylsteke, Maser states in Ammonia - Inversion, American Journal of Physics, 27, 554 (1959).

[28] S. Ladak, D. E. Read, G. K. Perkins, L. F. Cohen and W. R. Branford, Direct observation of magnetic monopole defects in an artificial spin-ice system, Nature Physics, 6, 359–363 (2010).

[29] T. Liu, R. Xue, B. Ding, D.A. Juraev, B.N. Saray, F. Soleymani, A novel and effective scheme for solving the fractional telegraph problem via the spectral element method. Fractal and Fractional, 8:12, 1–16 (2024).

[30] I.E. Niyozov, D.A. Juraev, R.F. Efendiev, M.J. Jalalov, The Cauchy problem for the system of elasticity. Journal of Contemporary Applied Mathematics, 14:2, 92–107 (2024).

Extension of the Gradient Effect on Eigenenergies to the “Electric Stern-Gerlach” Effect With Square of theLinearized Field

Authors

Downloads

Abstract

Keywords

Article Metrics

License

How to Cite

Similar Articles

Most read articles by the same author(s)

Submit Manuscript

Guide for Authors

Journal Info

Special Issues

Editors

Reviewers

Contact Us

Similar Articles

The Analytical Function Defined in the Hamilton-Jacobi and Schrödinger Approach and the Classical Schrödinger Equation

Dynamic and Nonlinear Analysis of Hybrid Epoxy Composites: Impact of Thickness, andTransient Behavior

Magnetic and Electric Fields, in the 400Kilovolt Electricity Transmission Lines, theImpact on the Environment

On The Solution of The Ill-Posed Cauchy Problem for Elliptic Systems of The First Order

A Class of Exponentially Fitted Finite Diﬀerence Scheme for Sin-gularly Perturbed Equations Involving Small Delays in Reaction and Convection Terms

Shape-Constrained Additive Modelling of Total Petroleum Hydrocarbon Contamination: A Simulation-Based Comparison within a Gamma–Log Framework

Experimental and Numerical Analysis of Annealing Effects in the Incremental Forming Process of Al1050 Aluminum Sheets

Biological Activation Constraints Enforce Robust Population Coding in Deep Neural Networks