Introducing the energy–density and local Schrödinger equations

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发表日期：

2025年5月5日

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Balakrishnan Viswanathan

摘要

It is generally accepted that the exact solution to the Schrödinger equation cannot be expressed as a single determinant of orbitals. This assertion is the result of the traditional approach taken to solve the N-electron problem in 3N dimensions, namely, integration over coordinates. Integration over coordinates averages the various interactions leading to approximations to the exact solution; this loss of local information is sought to be recovered through multi-determinant formalisms. We introduce the local Schrödinger equation (in ${\mathbb{R}}^{6}$ $R^{6}$ ) from the energy density representation of the Schrödinger equation (in ${\mathbb{R}}^{3N}$ $R^{3 N}$ ). A proof is presented that shows that there exists a single determinant representation (of one-electron orbitals) for the exact wavefunction that satisfies the Schrödinger equation. We also show that the exact orbitals that describe the system have the same orbital energy, thereby equalising the chemical potential within the system.