scholarly journals The $$\gamma$$ function in quantum theory II. Mathematical challenges and paradoxa

2021 ◽  
Author(s):  
Zs. É. Mihálka ◽  
M. Nooijen ◽  
Á. Margócsy ◽  
Á. Szabados ◽  
P. R. Surján
Keyword(s):  
Quantum Theory ◽  
Harmonic Oscillator ◽  
Gamma Function ◽  
Scientific Community ◽  
Quantum Mechanical ◽  
Generalized Function ◽  
Square Root ◽  
Traditional Function ◽  
Set Up ◽  
Simple Systems

AbstractWhile the square root of Dirac’s $$\delta$$ δ is not defined in any standard mathematical formalism, postulating its existence with some further assumptions defines a generalized function called $$\gamma (x)$$ γ ( x ) which permits a quasi-classical treatment of simple systems like the H atom or the 1D harmonic oscillator for which accurate quantum mechanical energies were previously reported. The so-defined $$\gamma (x)$$ γ ( x ) is neither a traditional function nor a distribution, and it remains to be seen that any consistent mathematical approaches can be set up to deal with it rigorously. A straightforward use of $$\gamma (x)$$ γ ( x ) generates several paradoxical situations which are collected here. The help of the scientific community is sought to resolve these paradoxa.

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

Quantum Narratives and the Power of Rhetorical Omission

2018 ◽  
Vol 48 (1) ◽  
pp. 24-55
Author(s):  
José G. Perillán
Keyword(s):  
Quantum Theory ◽  
Scientific Community ◽  
Fundamental Principle ◽  
International Scientific Community ◽  
Physics Community ◽  
Pilot Wave ◽  
History Of ◽  
Quantum Interpretation ◽  
History Of Quantum Theory ◽  
Pedagogical Discourses

John S. Bell openly questioned the dominance of an orthodox quantum interpretation that had seemingly raised the principle of indeterminism from an epistemological question to an ontological truth in the late 1920s. He understood the inevitability of indeterminism to be a theoretical choice made by the founding architects of quantum theory, not a fundamental principle of reality necessitated by experimental facts. As a result, Bell decried the general lull in quantum interpretation debates within the physics community, and in particular, the complete omission of Louis de Broglie’s deterministic pilot wave interpretation from all theoretical and pedagogical discourses. This paper reexamines the pilot wave’s rise, abandonment, and subsequent omission in the history of quantum theory. What emerges is not a straightforward story of victimization and hegemonic marginalization. Instead, it is a story that grapples with tensions between the polyphony of individual voices and a physics community’s evolving identity and consensus in response to particular sociopolitical and scientific contexts. At the heart of these tensions sits an international scientific community transitioning from a politically fractured and intellectually divergent community to one embracing a somewhat forced pragmatic convergence around rationally reconstructed narratives and concepts like the impossibility of determinism. The story of the pilot wave’s omission gives us a window into the inherent power that theoretical choice and a congealing rhetoric of orthodoxy have on a scientific community’s consensus, pedagogical canons, and the future development of science itself.

scholarly journals On individuality in quantum theory

2015 ◽  
Vol 13 (1) ◽  
pp. 29-38
Author(s):  
Jasmina Jeknic-Dugic
Keyword(s):  
Quantum Theory ◽  
Structural Realism ◽  
Mechanical Analysis ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Ontic Structural Realism

A quantum mechanical analysis of the decomposability of quantum systems into subsystems provides support for the so-called "attenuated Eliminative Ontic Structural Realism" within Categorical Structuralism studies in physics. Quantum subsystems are recognized as non-individual, relationally defined objects that deflate or relax some standard objections against Eliminative Ontic Structural Realism. Our considerations assume the universally valid quantum theory without tackling interpretational issues.

scholarly journals Pop-Science on the Internet: How ULISSE Makes the Ends Meet

10.28945/2459 ◽  
2002 ◽  
Author(s):  
Simona Cerrato
Keyword(s):  
Information Technology ◽  
General Public ◽  
Scientific Community ◽  
Scientific Information ◽  
High Technology ◽  
The Internet ◽  
High Quality ◽  
Increasing Demand ◽  
Set Up

There is an increasing demand for what we can call pop-science that is pertinent scientific information dedicated to the non-specialists. This demand comes both from professional categories and the general public. Simultaneously in the scientific community there is an increasing consciousness that diffusion of the scientific information is an asset the scientific community cannot afford to overlook. The Internet is a perfect tool to meet this demand. It reaches a large and ever-increasing number of people and permits an interactive and detailed exchange of information. As an experiment of how to combine high quality services and the information technology, we have set up Ulisse - In the net of science (http://ulisse.sissa.it), an innovative Italian project for the popularisation of science via the Internet. Its main purpose is to establish a connection between scientists and the general public. Ulisse is based on three major characteristics: a) high technology to create an efficient and friendly system, b) customisation of the services, c) a network of scientists, which guaranteed the quality of the materials.

scholarly journals Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 4 (1) ◽  
pp. 47-55
Author(s):  
Timothy Brian Huber
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Mechanical System ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Intertwining Operator

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

scholarly journals The ‘Astronomy for the Public’ Task Force

2012 ◽  
Vol 10 (H16) ◽  
pp. 550-551
Author(s):  
Carolina J. Ödman-Govender ◽  
Ian E. Robson
Keyword(s):  
Citizen Science ◽  
General Public ◽  
Scientific Community ◽  
Task Force ◽  
Scientific Thinking ◽  
The Public ◽  
Raising Awareness ◽  
Set Up ◽  
Force Range ◽  
The Universe

AbstractOne of the ways in which astronomy can stimulate development is by raising awareness of our place in the universe among the general public. This contributes to inspiring people and brings the scientific community and scientific thinking closer to everyone. The IAU OAD has set up one task force dedicated to ‘Astronomy for the Public’. Proposed activities of the task force range from low-tech astronomy outreach to citizen science. We will present the task force, its objectives and potential developmental impacts for the first few years of operation.

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