#### Document Type

Article

#### Publication Date

2017

#### Abstract

The Schrödinger theory for a system of electrons in the presence of both a static and time-dependent electromagnetic field is generalized so as to exhibit the intrinsic self-consistent nature of the corresponding Schrödinger equations. This is accomplished by proving that the Hamiltonian in the stationary-state and time-dependent cases {\hat{H}; \hat{H}(t)} are *exactly known* functionals of the corresponding wave functions {\Psi; \Psi(t)}, i.e. \hat{H} = \hat{H}[\Psi] and \hat{H}(t) = \hat{H}[\Psi(t)]. Thus, the Schrödinger equations may be written as \hat{H}[\Psi]\Psi = E[\Psi]\Psi and \hat{H}[\Psi(t)]\Psi(t) = i\partial\Psi(t)/\partial t. As a consequence the eiegenfunctions and energy eigenvalues {\Psi; E} of the stationary-state equation, and the wave function \Psi(t) of the temporal equation, can be determined self-consistently. The proofs are based on the 'Quantal Newtonian' first and second laws which are the equations of motion for the *individual* electron amongst the sea of electrons in the external fields. The generalization of the Schrödinger equation in this manner leads to additional new physics. The traditional description of the Schrödinger theory of electrons with the Hamiltonians {\hat{H}; \hat{H}(t)} known constitutes a special case.

#### Included in

Atomic, Molecular and Optical Physics Commons, Condensed Matter Physics Commons, Quantum Physics Commons

## Comments

This is the peer-reviewed version of the following article: V. Sahni.

J. Comput. Chem.2017, DOI: 10.1002/jcc.24888, which has been published in final form at http://dx.doi.org/10.1002/jcc.24888. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.