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Částicový model pro Higgsův kondensát a anomální geometrická difrakce
Souček, Jiří
In this paper we propose a particle model for the Higgs’ condensate: we propose that this condensate is the set of (infinite velocity) non-local tachyons. We show that then there exists the anomalous geometrical diffraction (which contradicts to quantum mechanics). We show that there exists a universal time constant which defines the limits of the validity of quantum mechanics. We propose an experiment testing the existence of the anomalous geometrical diffraction. We proposed the dark energy conjecture which enables to make an estimate of the time constant. We assume certain (“Feynman”) interaction between standard particle and the nonlocal tachyon. All this is related to the new (finite) form of the Feynman integral.
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Two new uncertainty relations and their applications
Lužová, Martina ; Skála, Lubomír (advisor) ; Kapsa, Vojtěch (referee)
The historical development of uncertainty relation, begining with first Heisenberg's thoughts of uncertainty principle is summed up in this thesis. After proving validity of Schwarz inequality general uncertainty relation for two hermitian operators is obtained, and from this general version the validity of Heisenberg uncertainty relation is than proved. The most important part of this work is the obtention of two new uncertainty relations, which are stronger then Heisenberg or Robertson-Schrödinger uncertainty relation, and their specific form for two examples - a free particle in a state discribed by the gaussian wave packet and the linear harmonic oscillator with a wave function in the shape of gaussian packet.
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Selected Solved Problems in Quantum Mechanics
Fišerová, Kateřina ; Bílek, Oldřich (advisor) ; Žák, Vojtěch (referee)
The main aim of this thesis was to create a set of problems in Quantum Mechanics, which would be included in a collection of solved problems in Physics available online on the website http://www.fyzikalniulohy.cz. As a result, thirty nine problems were completed, covering seven thematic areas partially of high school and mostly of introductory college Quantum Mechanics course. In general, the collection is mainly designed for college students as an exercise in basic quantum-mechanical problems and also for high school students, who have a desire to deal with some special problems. A detailed description of content, structure, and technical execution of this collection can be found in chapter 1 of this thesis. Another task was to review existing online collections of applets dealing with Quantum Mechanics. A selection of them is introduced in chapter 2 of this thesis.
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Hybrid-epistemický model kvantové mechaniky a možné řešení problému měření
Souček, Jiří
In this study we introduce and describe in details the hybrid-epistemic model for quantum mechanics. The main differences with respect to the standard model are following: (1) the measurement process is considered as an internal process inside quantum mechanics, i.e. it does not make a part of axioms and (2) the process of the observation of the state of the individual measuring system is introduced into axioms. The intrinsic measurement process is described in two variants (simplified and generalized). Our model contains hybrid, epistemic and hybrid-epistemic systems. Each hybrid system contains a unique orthogonal base composed from homogeneous (i.e. ontic) states. We show that in our model the measurement problem is consistently solvable. Our model represents the rational compromise between the Bohr’s view (the ontic model) and the Einstein’s view (the epistemic model).
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Obnovení lokality: axiomatická formulace modifikované kvantové mechaniky
Souček, Jiří
From the dichotomy "nonlocality vs non-realism" which is the consequence of Bell Inequalities (BI) we shall choose the non-realism. We shall present here the modified Quantum Mechanics (modQM) in the axiomatic form. ModQM was introduced in [5] and we shall show its non-realism in the description of an internal measurement process. ModQM allows the restoration of locality, since BI cannot be derived in it. In modQM it is possible to solve: the measurement problem, the collapse problem, the problem of a local model for EPR correlations (see[5]). ModQM is a unique explicit realization of non-realism in QM. ModQM should be preferred as an alternative to the standard QM mainly since it restores the locality.
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Nová axiomatizace kvantové mechaniky
Souček, Jiří
In this paper we describe a new (complete) axiomatization of quantum mechanics (QM) in which we add axioms describing the concept of an observation. We show that new axioms are clear and evident and based on common sense. Our approach is based on the idea of the observation of properties of an individual measuring system. We distinguish two concepts of a state: the properties of an individual measuring system and the state of an ensemble of systems. Then we prove that the ontic model of QM is inconsistent. This is our main result. This implies the necessity to consider “non-realistic” models for QM in which it is not true that each wave-function describes a possible state of an individual system. Our axiomatization is based on the postulate of the existence of definite outputs of an experiment. Thus the evident reality of the existence of definite outputs implies that our axiomatization is true and verifiable.
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Nová observační axiomatizace kvantové mechaniky, nekonsistence ontického modelu kvantové mechaniky a konec kvantové nelokality
Souček, Jiří
In this paper we describe a new axiomatization of quantum mechanics (QM) in which we replace the concept of the measurement by the concept of the observation. We shall describe and discuss this axiomatization in details. We show that new axioms are clear and evident and based on the common sense. Our approach is based on the idea of the observation of the individual state of the individual measuring system. We distinguish two concepts of a state: the individual state of the individual measuring system and the state of an ensemble of systems. Then we prove that the ontic model of QM (where the wave function describes the state of the individual system) is inconsistent. This is our main result. It implies that the "standard von Neumann's text-book QM" is inconsistent. This implies the necessity to consider "non-realistic" models for QM. Moreover we show that the proofs of Bell's theorem and of quantum nonlocality are not valid in these "nonrealistic" models for QM. This implies that there is no valid proof of the quantum nonlocality.
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The principle of anti-superposition in QM and the local solution of the Bell’s inequality problem
Souček, Jiří
In this paper we identify the superposition principle as a main source of problems in QM (measurement, collapse, non-locality etc.). Here the superposition principle for individual systems is substituted by the anti-superposition principle: no non-trivial superposition of states is a possible individual state (for ensembles the superposition principle is true). The modified QM is based on the anti-superposition principle and on the new type of probability theory (Extended Probability Theory [1]), which allows the reversible Markov processes as models for QM. In the modified QM the measurement is a process inside of QM and the concept of an observation of the measuring system is defined. The outcome value is an attribute of the ensemble of measured systems. The collapse of the state is substituted by the Selection process. We show that the derivation of Bell’s inequalities is then impossible and thus QM remains a local theory. Our main results are: the locality of the modified QM, the local explanation of EPR correlations, the non-existence of the wave-particle duality, the solution of the measurement problem. We show that QM can be understood as a new type of the statistical mechanics of many-particle systems.
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Exact methods in trade (model approximation)
Zeithamer, Tomáš ; Drozen, František (advisor) ; Jablonský, Josef (referee) ; Malý, Josef (referee) ; Kloc, Karel (referee)
The paper deals with quantum economy. It means the methods of quantum mechanics are applied in the study of economic processes. The scalar abstract economic quantities are constructed as follows: general abstract economic quantity F , average abstract economic quantity FA, marginal abstract economic quantity FM, marginal average abstract economic quantity FMA, average marginal abstract economic quantity FAM, elasticity of abstract economic quantity EF. All the abstract economic quantities mentioned above are constructed as mappings. The general theory of abstract economic quantities is utilized in a construction of the abstract total gross profit TGP. The set of static models of total gross profit TGP is constructed in the case that the first unit gross profit is slowly changed with time while the second unit gross profit is quickly changed with time in comparison with the first unit gross profit.
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