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The Schr(&)#246;dinger Equation with Coulomb Potential Admits no Exact Solutions

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Date Issued:
2019
Abstract/Description:
We prove that the Schr(&)#246;dinger equation with the electrostatic potential energy expressed by the Coulomb potential does not admit exact solutions for three or more bodies. It follows that the exact solutions proposed by Fock are flawed. The Coulomb potential is the problem. Based on the classical (non-quantum) principle of superposition, the Coulomb potential of a system of many particles is assumed to be the sum of all the pairwise Coulomb potentials. We prove that this is not accurate. The Coulomb potential being a hyperbolic (not linear) function, the superposition principle does not apply.The Schr(&)#246;dinger equation as studied in this PhD dissertation is a linear partial differential equation with variable coefficients. The only exception is the Schr(&)#246;dinger equation for the hydrogen atom, which is a linear ordinary differential equation with variable coefficients. No account is kept of the spin or the effects of the relativity.New electrostatic potentials are proposed for which the exact solutions of the Schr(&)#246;dinger equation exist. These new potentials obviate the need for the three-body force interpretations of the electrostatic potential.Novel methods for finding the exact solutions of the differential equations are proposed. Novel proof techniques are proposed for the nonexistence of the exact solutions of the differential equations, be they ordinary or partial, with constant or variable coefficients. Few novel applications of the established approximate methods of the quantum chemistry are reported. They are simple from the viewpoint of the quantum chemistry, but have some important aerospace engineering applications.
Title: The Schr(&)#246;dinger Equation with Coulomb Potential Admits no Exact Solutions.
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Name(s): Toli, Ilia, Author
Zou, Shengli, Committee Chair
Harper, James, Committee Member
Heider, Emily, Committee Member
Chen, Gang, Committee Member
Schulte, Alfons, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2019
Publisher: University of Central Florida
Language(s): English
Abstract/Description: We prove that the Schr(&)#246;dinger equation with the electrostatic potential energy expressed by the Coulomb potential does not admit exact solutions for three or more bodies. It follows that the exact solutions proposed by Fock are flawed. The Coulomb potential is the problem. Based on the classical (non-quantum) principle of superposition, the Coulomb potential of a system of many particles is assumed to be the sum of all the pairwise Coulomb potentials. We prove that this is not accurate. The Coulomb potential being a hyperbolic (not linear) function, the superposition principle does not apply.The Schr(&)#246;dinger equation as studied in this PhD dissertation is a linear partial differential equation with variable coefficients. The only exception is the Schr(&)#246;dinger equation for the hydrogen atom, which is a linear ordinary differential equation with variable coefficients. No account is kept of the spin or the effects of the relativity.New electrostatic potentials are proposed for which the exact solutions of the Schr(&)#246;dinger equation exist. These new potentials obviate the need for the three-body force interpretations of the electrostatic potential.Novel methods for finding the exact solutions of the differential equations are proposed. Novel proof techniques are proposed for the nonexistence of the exact solutions of the differential equations, be they ordinary or partial, with constant or variable coefficients. Few novel applications of the established approximate methods of the quantum chemistry are reported. They are simple from the viewpoint of the quantum chemistry, but have some important aerospace engineering applications.
Identifier: CFE0007733 (IID), ucf:52422 (fedora)
Note(s): 2019-08-01
Ph.D.
Sciences, Chemistry
Doctoral
This record was generated from author submitted information.
Subject(s): Schrodinger equation -- three body problem -- Fock -- helium -- analytical solutions -- exact solutions.
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0007733
Restrictions on Access: public 2019-08-15
Host Institution: UCF

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