3,486 research outputs found
Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential
We present an explicit convergent iterative solution for the lowest energy
state of the Schroedinger equation with a generalized double well potential
. The condition for the convergence of the
iteration procedure and the dependence of the shape of the groundstate wave
function on the parameter are discussed.Comment: 23 pages, 7 figure
Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation
The convergent iterative procedure for solving the groundstate Schroedinger
equation is extended to derive the excitation energy and the wave function of
the low-lying excited states. The method is applied to the one-dimensional
quartic potential problem. The results show that the iterative solution
converges rapidly when the coupling is not too small.Comment: 14 pages, 4 figure
Jarlskog Invariant of the Neutrino Mapping Matrix
The Jarlskog Invariant of the neutrino mapping matrix is
calculated based on a phenomenological model which relates the smallness of
light lepton masses and (of ) with the smallness of
violation. For small violating phase in the lepton sector,
is proportional to , but and are proportional
to . This leads to . Assuming
, we find
, consistent with the present experimental
data.Comment: 19 page
Compatible Quantum Theory
Formulations of quantum mechanics can be characterized as realistic,
operationalist, or a combination of the two. In this paper a realistic theory
is defined as describing a closed system entirely by means of entities and
concepts pertaining to the system. An operationalist theory, on the other hand,
requires in addition entities external to the system. A realistic formulation
comprises an ontology, the set of (mathematical) entities that describe the
system, and assertions, the set of correct statements (predictions) the theory
makes about the objects in the ontology. Classical mechanics is the prime
example of a realistic physical theory. The present realistic formulation of
the histories approach originally introduced by Griffiths, which we call
'Compatible Quantum Theory (CQT)', consists of a 'microscopic' part (MIQM),
which applies to a closed quantum system of any size, and a 'macroscopic' part
(MAQM), which requires the participation of a large (ideally, an infinite)
system. The first (MIQM) can be fully formulated based solely on the assumption
of a Hilbert space ontology and the noncontextuality of probability values,
relying in an essential way on Gleason's theorem and on an application to
dynamics due in large part to Nistico. The microscopic theory does not,
however, possess a unique corpus of assertions, but rather a multiplicity of
contextual truths ('c-truths'), each one associated with a different framework.
This circumstance leads us to consider the microscopic theory to be physically
indeterminate and therefore incomplete, though logically coherent. The
completion of the theory requires a macroscopic mechanism for selecting a
physical framework, which is part of the macroscopic theory (MAQM). Detailed
definitions and proofs are presented in the appendice
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