Papers by OLAVO LEOPOLDINO DA S FILHO
In our previous papers we were interested in making a reconstruction of quantum mechanics accordi... more In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum mechanics itself---that is, the formation of operators. We then investigate all the subtleties involved in forming operators from their classical counterparts. We show, using the formalism of quantum phase-space distributions, that our formation method, which is equivalent to Weyl's rule, gives the correct answer. Since this method implies that eigenstates are not dispersion-free we argue for modifications in the orthodox view. Many properties of the quantum phase-space distributions are also investigated and discussed in the realm of our classical approach. We then strengthen the conclusions of our previous papers that quantum mechanics is merely an extremely good approximation of classical statistical mechanics performed upon the configuration space
Quantum mechanics as a classical theory; 4, the negative mass conjecture
The following two papers form a natural development of a previous series of three articles on the... more The following two papers form a natural development of a previous series of three articles on the foundations of quantum mechanics; they are intended to take the theory there developed to its utmost logical and epistemological consequences. We show in the first paper that relativistic quantum mechanics might accommodate without ambiguities the notion of negative masses. To achieve this, we rewrite all of its formalism for integer and half integer spin particles and present the world revealed by this conjecture. We also base the theory on the second order Klein-Gordon's and Dirac's equations and show that they can be stated with only positive definite energies. In the second paper we show that the general relativistic quantum mechanics derived in paper II of this series supports this conjecture
We present in this continuation paper a new axiomatic derivation of the Schrödinger equation from... more We present in this continuation paper a new axiomatic derivation of the Schrödinger equation from three basic postulates. This new derivation sheds some light on the thermodynamic character of the quantum formalism. We also show the formal connection between this derivation and the one previously done by other means. Some considerations about metaestability are also drawn. We return to an example previously developed to show how the connection between both derivations works
The Use of Systems Dynamics for Energy and Environmental Education
arXiv: Quantum Physics, 1996
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal In... more In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we wish. This result is necessary if one even think about making general relativistic extensions of the quantum formalism. Besides, physics shall not be dependent on the specific representation we use and this result is necessary to make quantum theory consistent and complete.
In these continuation papers (VI and VII) we are interested in approach the problem of spin from ... more In these continuation papers (VI and VII) we are interested in approach the problem of spin from a classical point of view. In this first paper we will show that the spin is neither basically relativistic nor quantum but reflects just a simmetry property related to the Lie algebra to which it is associated. The classical approach will be paraleled with the usual quantum one to stress their formal similarities and epistemological differences. The important problem of Einstein-Bose condensation for fermions will also be addressed.
Physical Review B, 2007
Nonperturbative, accurate variational results for the binding energy of a shallow hydrogenic impu... more Nonperturbative, accurate variational results for the binding energy of a shallow hydrogenic impurity in a bulk semiconductor irradiated by a high-frequency, intense laser field are presented. It is pointed out that variational results found with 1s and 2s atomic trial wave functions presented in previous works on this subject are incorrect because these wave functions do not allow the stretching of the electronic cloud along the polarization direction. This is corrected here by choosing appropriate trial wave functions for the ground and first excited states, which resemble those for the ͑1s͒ states of the H 2 + molecular ion. Special attention is paid to the limit of large values for the laser-dressing parameter ␣ 0 , where our model furnishes almost exact results. In this limit, we found that the binding energy tends to −1 / 4 Ry * with the increase of ␣ 0. Then, impurity stability against ionization is expected, which is in contrast to previous works.
In our previous papers we were interested in making a reconstruction of quantum mechanics accordi... more In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum mechanics itself---that is, the formation of operators. We then investigate all the subtleties involved in forming operators from their classical counterparts. We show, using the formalism of quantum phase-space distributions, that our formation method, which is equivalent to Weyl's rule, gives the correct answer. Since this method implies that eigenstates are not dispersion-free we argue for modifications in the orthodox view. Many properties of the quantum phase-space distributions are also investigated and discussed in the realm of our classical approach. We then strengthen the conclusions of our previous papers that quantum mechanics is merely an extremely good approximation of classical statistical mechanics performed upon the configuration s...
Magnetic investigation of iron-nitride-based magnetic fluid
Hyperfine Interactions, 2007
ABSTRACT
Arxiv preprint quant-ph/9503025, Mar 28, 1995
In this continuation paper, we apply the general relativistic quantum theory for one particle sys... more In this continuation paper, we apply the general relativistic quantum theory for one particle systems, derived in paper II of this series, to a simple problem: the quantum Schwartzchild problem, where one particle of mass {\it m% } gravitates around a massive body. The results thus obtained reveal that, in the realm of such a theory, the negative mass conjecture we made in paper IV of this series is, indeed, adequate. It is shown that gravitation is responsible for the loss of energy quantization. We relate this property with the ideas of irreversibility and time arrow.
Foundations of Quantum Mechanics: The Connection Between QM and the Central Limit Theorem
Foundations of Physics, 2004
In this paper we unravel the connection between the quantum mechanical formalism and the Central ... more In this paper we unravel the connection between the quantum mechanical formalism and the Central limit theorem (CLT). We proceed to connect the results coming from this theorem with the derivations of the Schrödinger equation from the Liouville equation, presented by ourselves in other papers. In those papers we had used the concept of an infinitesimal parameter δx that raised some controversy. The status of this infinitesimal parameter is then elucidated in the framework of the CLT. Finally, we use the formal apparatus developed in our previous papers and the results of the present one to advance an alternative objective interpretation of quantum mechanics in which its relations with the classical framework are made explicit. The relations between our approach and those using the Wigner–Moyal transformation are also addressed.
Quantum mechanics as a classical theory; 11, thermodynamics and equilibrium
In this continuation paper the theory is further extended to reveal the connection between its fo... more In this continuation paper the theory is further extended to reveal the connection between its formal aparatus, dealing with microscopic quantities, and the formal aparatus of thermodynamics, related to macroscopic properties of large systems. We will also derive the Born-Sommerfeld quantization rules from the formalism of the infinitesimal Wigner-Moyal transformations and, as a consequence of this result, we will also make a connection between the later and the path integral approach of Feynman. Some insights of the relation between quantum mechanics and equilibrium states will be given as a natural development of the interpretation of the above results
Quantum mechanics as a classical theory; 8, second quantization
We continue in this paper our program of rederiving all quantum mechanical formalism from the cla... more We continue in this paper our program of rederiving all quantum mechanical formalism from the classical one. We now turn our attention to the derivation of the second quantized equations, both for integral and half-integral spins. We then show that all the quantum results may be derived using our approach and also show the interpretation suggested by this derivation. This paper may be considered as a first approach to the study of the quantum field theory beginning by the same classical ideas we are supporting since the first paper of this series
Quantum Mechanics as a Classical Theory; 13, The Tunnel Effect
In this continuation paper we will address the problem of tunneling. We will show how to settle t... more In this continuation paper we will address the problem of tunneling. We will show how to settle this phenomenon within our classical interpretation. It will be shown that, rigorously speaking, there is no tunnel effect at all
Quantum Mechanics as a Classical Theory; 16, Positive-Definite Densities
In this paper we will turn our attention to the problem of obtaining phase-space probability dens... more In this paper we will turn our attention to the problem of obtaining phase-space probability density functions. We will show that it is possible to obtain functions which assume only positive values over all its domain of definition
Quantum mechanics as a classical theory; 2, relativistic theory
In this article, the axioms presented in the first one are reformulated according to the special ... more In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for both the density function and the probability amplitude. It is shown that, within the present theory's scope, Dirac's second order equation should be considered the fundamental one in spite of the first order equation. A relativistic expression is obtained for the statistical potential. Axioms are again altered and made compatible with the general theory of relativity. These postulates, together with the idea of the statistical potential, allow us to obtain a general relativistic quantum theory for {\it ensembles} composed of single particle systems
Zero-field birefringence in magnetic fluids: Temperature, particle size, and concentration dependence
Journal of Applied Physics, 2000
ABSTRACT
arXiv: Quantum Physics, 1997
In this paper we will turn our attention to the problem of obtaining phase-space probability dens... more In this paper we will turn our attention to the problem of obtaining phase-space probability density functions. We will show that it is possible to obtain functions which assume only positive values over all its domain of definition.
Redes predicativas e inferências lexicais (Uma alternativa à lógica formal na análise
In this continuation paper the Schr\"odinger equation for the half-integral spin eigenfuncti... more In this continuation paper the Schr\"odinger equation for the half-integral spin eigenfunctions is obtained and solved. We show that all the properties already derived using the Heisemberg matrix calculation and Pauli's matrices are also obtained in the realm of these analytical functions. We also show that Einstein-Bose condensation for fermions is expected. We then conclude this series of two papers on the concept of classical spin.
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Papers by OLAVO LEOPOLDINO DA S FILHO