II . Functional Quantum Mechanics and the Equivalence with a Product of Schrödinger Problems
نویسنده
چکیده
The New Tamm-Dancoff procedure consists of three main parts: an expansion for pairs of states with respect to a non-orthogonal base, a cut-off approximation for this expansion, and a transformation with respect to a new reference state. In this paper we treat part one and two. It is shown that the NTD-procedure is equivalent to the tensor product of the original Schrödinger problem and its conjugate problem. The occurring nonlinear transformation is examined and the cut-off is discussed.
منابع مشابه
Analytical Soliton Solutions Modeling of Nonlinear Schrödinger Equation with the Dual Power Law Nonlinearity
Introduction In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schrödinger equations, called the nonlinear Schrödinger equation with the dual power law nonlinearity. Given the widespread use of the Schrödinger equation in physics and e...
متن کاملAsymptotic Behavior to the 3-d Schrödinger/hartree Poisson and Wigner Poisson Systems
Using an appropriate scaling group for the 3-D Schrödinger–Poisson equation and the equivalence between the Schrödinger formalism and the Wigner representation of quantum mechanics it is proved that, when time goes to infinity, the limit of the rescaled self-consistent potential can be identified as the Coulomb potential. As a consequence, Schrödinger–Poisson and Wigner–Poisson systems are asym...
متن کاملA brief history of the mathematical equivalence between the two quantum mechanics
The aim of this paper is to give a brief account of the development of the mathematical equivalence of quantum mechanics. In order to deal with atomic systems, Heisenberg developed matrix mechanics in 1925. Some time later, in the winter of 1926, Schrödinger established his wave mechanics. In the spring of 1926, quantum physicists had two theoretical models that allowed them to predict the same...
متن کاملDirichlet problems for stationary von Neumann-Landau wave equations
It is known that von Neumann-Landau wave equation can present a mathematical formalism of motion of quantum mechanics, that is an extension of Schrödinger's wave equation. In this paper, we concern with the Dirichlet problem of the stationary von Neumann-Landau wave equation: where Ω is a bounded domain in R n. By introducing anti-inner product spaces, we show the existence and uniqueness of th...
متن کاملThe Equivalence Principle of Quantum Mechanics: Uniqueness Theorem
Recently we showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = ∂qS0 and exploits a basic GL(2, C)–symmetry which underlies the canonical formalism. In particular, we looked for the special transformations leading to the free system with vanishing energy. Furthermore, we saw tha...
متن کامل