5 years ago

Generalization of the Schrödinger theory of electrons

Generalization of the Schrödinger theory of electrons
Viraht Sahni
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 {Ĥ;Ĥ(t)} are exactly known functionals of the corresponding wave functions {Ψ;Ψ(t)}, that is, Ĥ=Ĥ[Ψ] and Ĥ(t)=Ĥ[Ψ(t)]. Thus, the Schrödinger equations may be written as Ĥ[Ψ]Ψ=E[Ψ]Ψ and Ĥ[Ψ(t)]Ψ(t)=i∂Ψ(t)/∂t. As a consequence the eiegenfunctions and energy eigenvalues {Ψ,E} of the stationary-state equation, and the wave function Ψ(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 {Ĥ;Ĥ(t)} known constitutes a special case. © 2017 Wiley Periodicals, Inc. The Schrödinger theory of electrons in electromagnetic fields is generalized via the “Quantal Newtonian” second and first laws to exhibit the intrinsic self-consistent nature of the time-dependent and stationary-state equations.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1002/jcc.24888

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.