547 research outputs found
Trajectories in the Context of the Quantum Newton's Law
In this paper, we apply the one dimensional quantum law of motion, that we
recently formulated in the context of the trajectory representation of quantum
mechanics, to the constant potential, the linear potential and the harmonic
oscillator. In the classically allowed regions, we show that to each classical
trajectory there is a family of quantum trajectories which all pass through
some points constituting nodes and belonging to the classical trajectory. We
also discuss the generalization to any potential and give a new definition for
de Broglie's wavelength in such a way as to link it with the length separating
adjacent nodes. In particular, we show how quantum trajectories have as a limit
when the classical ones. In the classically forbidden regions,
the nodal structure of the trajectories is lost and the particle velocity
rapidly diverges.Comment: 17 pages, LateX, 6 eps figures, minor modifications, Title changed,
to appear in Physica Script
On the linearization of the generalized Ermakov systems
A linearization procedure is proposed for Ermakov systems with frequency
depending on dynamic variables. The procedure applies to a wide class of
generalized Ermakov systems which are linearizable in a manner similar to that
applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into
this category but others, more generic, systems are also included
Unitary relations in time-dependent harmonic oscillators
For a harmonic oscillator with time-dependent (positive) mass and frequency,
an unitary operator is shown to transform the quantum states of the system to
those of a harmonic oscillator system of unit mass and time-dependent
frequency, as well as operators. For a driven harmonic oscillator, it is also
shown that, there are unitary transformations which give the driven system from
the system of same mass and frequency without driving force. The transformation
for a driven oscillator depends on the solution of classical equation of motion
of the driven system. These transformations, thus, give a simple way of finding
exact wave functions of a driven harmonic oscillator system, provided the
quantum states of the corresponding system of unit mass are given.Comment: Submitted to J. Phys.
The Equivalence Postulate of Quantum Mechanics
The Equivalence Principle (EP), stating that all physical systems are
connected by a coordinate transformation to the free one with vanishing energy,
univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories
depend on the Planck length through hidden variables which arise as initial
conditions. The formulation has manifest p-q duality, a consequence of the
involutive nature of the Legendre transform and of its recently observed
relation with second-order linear differential equations. This reflects in an
intrinsic psi^D-psi duality between linearly independent solutions of the
Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even
for bound states. No use of any axiomatic interpretation of the wave-function
is made. Tunnelling is a direct consequence of the quantum potential which
differs from the usual one and plays the role of particle's self-energy. The
QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of
the extended real line. This is an important feature as the L^2 condition,
which in the usual formulation is a consequence of the axiomatic interpretation
of the wave-function, directly follows as a basic theorem which only uses the
geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP.
As a result, the EP itself implies a dynamical equation that does not require
any further assumption and reproduces both tunnelling and energy quantization.
Several features of the formulation show how the Copenhagen interpretation
hides the underlying nature of QM. Finally, the non-stationary higher
dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the
action of SL(2,R) subgroups acting on the reduced action explicitly reveals
that the wave-function describes only equivalence classes of Planck length
deterministic physics. New derivation of the Schwarzian derivative from the
cocycle condition. "Legendre brackets" introduced to further make "Legendre
duality" manifest. Introduction now contains examples and provides a short
pedagogical review. Clarifications, conclusions, ackn. and references adde
Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator
For Dirac equation, operator-invariants containing explicit time-dependence
in parallel to known time-dependent invariants of nonrelativistic Schr\"odinger
equation are introduced and discussed. As an example, a free Dirac particle is
considered and new invariants are constructed for it. The integral of motion,
which is initial Newton-Wigner position operator, is obtained explicitly for a
free Dirac particle. For such particle with kick modeled by delta-function of
time, the time-depending integral, which has physical meaning of initial
momentum, is found.Comment: LATEX,21 pages,submitted to Physica Script
Management accounting of agricultural production: improving planning and standardization of costs in the management information system
The problems of organizing effective management accounting of agricultural production through the widespread use of economic methods, both production management and accounting and management methods and the development of their information functions, are very relevant and necessary. Management accounting in modern times is a universal integrated mechanism for the accounting and management activities of an agricultural organization. The management accounting information system should be oriented towards solving complex issues and making managerial decisions quickly. The purpose of the study is the rationale for rationing, planning and management accounting of costs, their control and analysis of production results in the agricultural management information system. The subject of the study is management accounting, while principles are formulated and new methods for rationing labor, material and biological costs of agricultural production are proposed. A unified nomenclature of cost items has been developed for planning, managerial accounting, analysis and control, both for individual production, accounting and planning objects, as well as for self-supporting units (responsibility centers) and the organization as a whole. For the organization of rationing, planning and management accounting of production costs, the sequence of implementation of special procedures is defined, a unified nomenclature of cost items is developed based on the basic conditions of requirements, which include classification attributes, degree of cost participation in the creation of new products, cost control by hierarchical levels of management. It is concluded that by comparing the actual and planned costs for the production of a particular object of planning and accounting, it is possible to analyze their cause and effect deviations, deviations of the actual marginal income and operating profit of the production of these products from their normative values by changing each specific cost item
Lie symmetries for two-dimensional charged particle motion
We find the Lie point symmetries for non-relativistic two-dimensional charged
particle motion. These symmetries comprise a quasi-invariance transformation, a
time-dependent rotation, a time-dependent spatial translation and a dilation.
The associated electromagnetic fields satisfy a system of first-order linear
partial differential equations. This system is solved exactly, yielding four
classes of electromagnetic fields compatible with Lie point symmetries
Schemes of implementation in NMR of quantum processors and Deutsch-Jozsa algorithm by using virtual spin representation
Schemes of experimental realization of the main two qubit processors for
quantum computers and Deutsch-Jozsa algorithm are derived in virtual spin
representation. The results are applicable for every four quantum states
allowing the required properties for quantum processor implementation if for
qubit encoding virtual spin representation is used. Four dimensional Hilbert
space of nuclear spin 3/2 is considered in details for this aimComment: 15 pages, 3 figure
Estimating Temperature Fluctuations in the Early Universe
A lagrangian for the essence field is constructed for a constant scalar
potential and its form determined when the scale factor was very small compared
to the present epoch but very large compared to the inflationary epoch. This
means that one is already in an expanding and flat universe. The form is
similar to that of an oscillator with time-dependent frequency. Expansion is
naturally built into the theory with the existence of growing classical
solutions of the scale factor. The formalism allows one to estimate
fluctuations of the temperature of the background radiation in these early
stages (compared to the present epoch) of the universe. If the temperature at
time is and at time the temperature is
(), then for small times, the probability for the logarithm of
inverse temperature evolution can be estimated to be given by
where
, is the Planck mass and Planck's constant and the
speed of light has been put equal to unity. There is the further possibility
that a single scalar field may suffice for an inflationary scenario as well as
the dark matter and dark energy realms.Comment: 8 pages, Revtex, title,abstract and format changed for journal
publication,no change in basic results, clarifications and a figure added.
Keywords: physics of the early universe,inflation, dark matter theory, dark
energy theory. PACS: 95.35.+d ; 95.36.+x ; 98.80.Cq ; 98.80.-
- …