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Charge symmetry of wave functions for an electron in a quantized electromagnetic wave field

Mikhail Vladimirovich Fedorov

Russian Physics JournalJun 1, 19750 citations

Wave Functions for Harmonically Bound Electrons in an Electromagnetic Field

Viraht Sahni

Springer tracts in modern physicsJan 1, 20220 citations

Permutation symmetry of wave functions of a system of identical particles

M. F. Sarry

Journal of Experimental and Theoretical PhysicsOct 1, 19793 citations

Proof of the Wave Function Identity, a New Symmetry Constraint for the Three-Electron Quantum Dot in a Magnetic Field and Ad Hoc Generalization to Bound Many-Electron Systems

Marlina Slamet, Viraht Sahni

We prove the Wave Function Identity (WFI), a new symmetry constraint on the solutions of the Schrödinger-Pauli equation for the Coulombically interacting N = 3 electron 2-dimensional harmonically bound ‘artificial atom’ or quantum dot in a uniform magnetic field. The symmetry is comprised of an interchange of the spatial coordinates of two electrons whilst keeping their spin moments unchanged, followed by an inversion of all three electron coordinates. The proof is achieved by first deriving the general form of the exact correlated wave function in the high-electron-correlation Wigner regime and then proving the WFI employing this form for a quartet state. The satisfaction of the Pauli principle (PP) and the odd parity of this state are also proved. An exact closed-form analytical expression for a quartet state in the Wigner regime is derived, and the properties of the PP, WFI, parity and other properties exhibited diagrammatically. Together with our prior proof of the WFI for the N = 2 electron case, we propose ad hoc the validity of the WFI for all bound-state N ≥ 2 electron systems for arbitrary symmetric binding potential, arbitrary electron-interaction of the form ω(|r – r’|) and arbitrary dimensionality.We prove the Wave Function Identity (WFI), a new symmetry constraint on the solutions of the Schrödinger-Pauli equation for the Coulombically interacting N = 3 electron 2-dimensional harmonically bound ‘artificial atom’ or quantum dot in a uniform magnetic field. The symmetry is comprised of an interchange of the spatial coordinates of two electrons whilst keeping their spin moments unchanged, followed by an inversion of all three electron coordinates. The proof is achieved by first deriving the general form of the exact correlated wave function in the high-electron-correlation Wigner regime and then proving the WFI employing this form for a quartet state. The satisfaction of the Pauli principle (PP) and the odd parity of this state are also proved. An exact closed-form analytical expression for a quartet state in the Wigner regime is derived, and the properties of the PP, WFI, parity and other properties exhibited diagrammatically. Together with our prior proof of the WFI for the N = 2 electron case, we propose ad hoc the validity of the WFI for all bound-state N ≥ 2 electron systems for arbitrary symmetric binding potential, arbitrary electron-interaction of the form ω(|r – r’|) and arbitrary dimensionality.

AxiomsOct 16, 20260 citations

SYMMETRIES AND WAVE FUNCTIONS

WORLD SCIENTIFIC eBooksJul 1, 20010 citations

A secondary solution of the Schrödinger and Klein-Gordon equations in modeling atomic, molecular and electrodynamic systems

Alexandru Popa

We study atomic and molecular (AM) stationary systems and electrodynamic (ED) systems, composed of an electron interacting with an electromagnetic field. We show that the Schr?dinger and Klein-Gordon equations written for these systems have a secondary solution, which is the wave function associated to a classical system. For AM systems, the wave surfaces (S surfaces) and their normals (C curves) are solutions of the Hamilton-Jacobi equation, written for the same system. The S surfaces have a periodical motion and the C curves are closed. The integral relation of the Schr?dinger equation on the C curve has a solution identical to the wave function associated to the classical motion. This solution leads to the generalized Bohr quantization relation and to the generalized de Broglie relations, which are valid in the space of the electron coordinates. An identical wave function verifies the Klein-Gordon equation, in the case of the EM systems. The above properties lead to a central field method for calculation of the energetic values and symmetry properties for AM systems, whose accuracy is comparable to the accuracy of the Hartree-Fock method. They also lead to an accurate method for modeling EM systems, which is verified by experimental data from the literature. The above properties are deduced without using any approximation.We study atomic and molecular (AM) stationary systems and electrodynamic (ED) systems, composed of an electron interacting with an electromagnetic field. We show that the Schr?dinger and Klein-Gordon equations written for these systems have a secondary solution, which is the wave function associated to a classical system. For AM systems, the wave surfaces (S surfaces) and their normals (C curves) are solutions of the Hamilton-Jacobi equation, written for the same system. The S surfaces have a periodical motion and the C curves are closed. The integral relation of the Schr?dinger equation on the C curve has a solution identical to the wave function associated to the classical motion. This solution leads to the generalized Bohr quantization relation and to the generalized de Broglie relations, which are valid in the space of the electron coordinates. An identical wave function verifies the Klein-Gordon equation, in the case of the EM systems. The above properties lead to a central field method for calculation of the energetic values and symmetry properties for AM systems, whose accuracy is comparable to the accuracy of the Hartree-Fock method. They also lead to an accurate method for modeling EM systems, which is verified by experimental data from the literature. The above properties are deduced without using any approximation.

Journal of Physics Conference SeriesMar 11, 20140 citations

Wave function identity: A new symmetry for 2-electron systems in an electromagnetic field

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