A generalized Schrödinger equation via a complex Lagrangian of electrodynamics
- DOI
- 10.1080/14029251.2015.1056619How to use a DOI?
- Keywords
- Schrödinger equation; complex Lagrangian; ℒ– duality; complex relativistic Hamiltonian
- Abstract
In this paper we give a generalized form of the Schrödinger equation in the relativistic case, which contains a generalization of the Klein-Gordon equation. By complex Legendre transformation, the complex Lagrangian of electrodynamics produces a complex relativistic Hamiltonian H of electrodynamics, on the holomorphic cotangent bundle T′* M. By a special quantization process, a relativistic time dependent Schrödinger equation, in the adapted frames of (T′* M, H) is obtained. This generalized Schrödinger equation can be expressed with respect to the Laplace operator of the complex Hamilton space (T′*M, H). Finally, under some additional conditions on the proper time s of the complex space-time M and the time parameter t along the quantum state, by the method of separation of variables, we obtain two classes of solutions for the Schrödinger equation, one for the weakly gravitational complex curved space M, and the second in the complex space-time with Schwarzschild metric.
- Copyright
- © 2015 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Nicoleta Aldea AU - Gheorghe Munteanu PY - 2021 DA - 2021/01/06 TI - A generalized Schrödinger equation via a complex Lagrangian of electrodynamics JO - Journal of Nonlinear Mathematical Physics SP - 361 EP - 373 VL - 22 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2015.1056619 DO - 10.1080/14029251.2015.1056619 ID - Aldea2021 ER -