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QUANTUM MECHANICS.

Sadikova Nargiza Bakhtiorovna Tursunova Zukhra Botyrovna

Published Oct 15, 2022• 0 citations
Publisher

Abstract

This article gives a brief information to quantum mechanics. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. The descriptor “quantum” arises because in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take on continuous values, as we’ll see.

DOI
10.5281/zenodo.7207705

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This article gives a brief information to quantum mechanics. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. The descriptor “quantum” arises because in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take on continuous values, as we’ll see.
An interpretation of quantum mechanics in terms of classical concepts, ``beables,'' due to de Broglie, Bohm, and Bell (BBB) is generalized and further developed. By assuming that all physical quantities take discrete values on sufficiently small scales, we can use this interpretation to give trajectories for all possible quantities, including the position of a particle, its spin, etc. When applied to position, it is shown that, in the continuum limit, this interpretation reduces to the causal one of Bohm. As an illustration, the BBB trajectories are computed explicitly in two simple models.
Quantum mechanics (or simply quantum physics) is the branch of physics that applies to particles and systems of particles, such as atoms and molecules. In that realm the laws of classical mechanics and classical electromagnetism break down, and only quantum mechanics provides the concepts and computational methods that explain observed phenomena. Quantum mechanics uses specially developed tools, such as wave functions, that contain all of the relevant information about particles and systems. is approach is needed to understand the true nature of electromagnetic radiation and how that radiation interacts with matter. e mathematics used in quantum mechanics is highly specialized and often complex. In this chapter we’ll address some of the key questions that require quantum mechanics without presenting the full mathematical formalism. e important questions we’ll address all deal with observable physical phenomena. We’ll discuss how quantum mechanics is used to answer these questions but will omit the advanced mathematical details.
Quantum mechanics is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Quantum mechanics is inescapable. Nearly all fields of modern physics, from elementary particles to the big bang, from semiconductors to solar energy cells, are related to quantum physics. Particles have characteristic trait of both particles and waves. The Schrodinger equation is the basic equation of quantum mechanics. The Schrodinger equation was established based on the quantization of energy conservation using quantum operators and the de Broglie relation. Wave function plays an important role in quantum mechanics. The probability interpretation assumes that the norm of the wave function measures the probability of the system in a particular coordinate or representation, in which the total probability is normalized.
Abstract Grothendieck’s bound is used in the context of a single quantum system, in contrast to previous work which used it for multipartite entangled systems and the violation of Bell-like inequalities. Roughly speaking the Grothendieck theorem considers a ‘classical’ quadratic form C that uses complex numbers in the unit disc, and takes values less than 1. It then proves that if the complex numbers are replaced with vectors in the unit ball of the Hilbert space, then the ‘quantum’ quadratic form Q might take values greater than 1, up to the complex Grothendieck constant k G . The Grothendieck theorem is reformulated here in terms of arbitrary matrices (which are multiplied with appropriate normalisation prefactors), so that it is directly applicable to quantum quantities. The emphasis in the paper is in the ‘Grothendieck region’ ( 1 , k G ) , which is a classically forbidden region in the sense that C cannot take values in it. Necessary (but not sufficient) conditions for Q taking values in the Grothendieck region are given. Two examples that involve physical quantities in systems with six and 12-dimensional Hilbert space, are shown to lead to Q in the Grothendieck region ( 1 , k G ) . They involve projectors of the overlaps of novel generalised coherent states that resolve the identity and have a discrete isotropy.
Quantum Mechanics is one of the most important scientific developments of the twentieth century. It serves as the basis for understanding how matter and energy behave on very small scales. Unlike classical mechanics, quantum mechanics explains physical phenomena through probabilistic models, wave functions, operators, and discrete quantized states. This paper offers a thorough study of the fundamentals of quantum mechanics, covering its historical background, postulates, mathematical framework, wave-particle duality, Schrödinger equation, uncertainty principle, and operator theory. The paper also looks at how quantum mechanics is used in modern technologies such as quantum computing, lasers, semiconductors, and medical imaging. The goal of this paper is to provide a clear and detailed foundation for students and researchers who want to grasp the main principles of quantum theory. General Terms Quantum Mechanics, Physics, Wave Function, Uncertainty, Quantum Theory, Measurement, Operators.