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Quantum Gravity: Mathematical Models and Experimental Bounds

pradeep — Sun, 26 Nov 2017 14:46:27 GMT

Quantum Gravity: Mathematical Models and Experimental Bounds
Bertfried Fauser, Jürgen Tolksdorf, Eberhard Zeidler,
English | 2006-12-12 | ISBN: 3764379774 | 336 pages | PDF | 3.8 mb

This book provides the reader with an overview of the different mathematical attempts to quantize gravity written by leading experts in this field. Also discussed are the possible experimental bounds on quantum gravity effects. The contributions have been strictly refereed and are written in an accessible style. The present volume emerged from the 2nd Blaubeuren Workshop "Mathematical and Physical Aspects of Quantum Gravity".

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Electrothermal Analysis of VLSI Systems

pradeep — Wed, 27 Sep 2017 02:34:12 GMT

Electrothermal Analysis of VLSI SystemsByYi-Kan Cheng, Ching-Han Tsai, Chin-Chi Teng
2002 | 217 Pages | ISBN: 079237861X | PDF | 7 MB

This useful book addresses electrothermal problems in modern VLSI systems. It discusses electrothermal phenomena and the fundamental building blocks that electrothermal simulation requires. The authors present three important applications of VLSI electrothermal analysis: temperature-dependent electromigration diagnosis, cell-level thermal placement, and temperature-driven power and timing analysis.

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Quantum Groups: A Path to Current Algebra

pradeep — Wed, 27 Sep 2017 02:33:09 GMT

Quantum Groups: A Path to Current Algebra
Ross Street,
English | 2007-01-29 | ISBN: 0521695244 | 260 pages | PDF | 1.4 mb

Algebra has moved well beyond the topics discussed in standard undergraduate texts on modern algebra. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However is written for the reader at ease with at least one such structure and keen to learn the latest algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an algebra. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a coalgebra. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term quantum group, along with revolutionary new examples, was launched by Drinfeld in 1986.

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Quantum Dot Devices

pradeep — Tue, 11 Feb 2014 16:23:34 GMT

Quantum Dot Devices
By Zhiming M. Wang
2012 | 374 Pages | ISBN: 1461435692 | PDF | 13 MB

Quantum dots as nanomaterials have been extensively investigated in the past several decades from growth to characterization to applications. As the basis of future developments in the field, this book collects a series of state-of-the-art chapters on the current status of quantum dot devices and how these devices take advantage of quantum features. Written by 56 leading experts from 14 countries, the chapters cover numerous quantum dot applications, including lasers, LEDs, detectors, amplifiers, switches, transistors, and solar cells. is appropriate for researchers of all levels of experience with an interest in epitaxial and/or colloidal quantum dots. Itprovides the beginner with the necessary overview of this exciting field and those more experienced with a comprehensive reference source.

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Quantum mechanics

pradeep — Fri, 14 Oct 2011 14:26:30 GMT

Free particle

For example, consider a free particle. In quantum mechanics, there is wave-particle duality so the properties of the particle can be described as the properties of a wave. Therefore, its quantum state can be represented as a wave of arbitrary shape and extending over space as a wave function. The position and momentum of the particle are observables. The Uncertainty Principle states that both the position and the momentum cannot simultaneously be measured with full precision at the same time. However, one can measure the position alone of a moving free particle creating an eigenstate of position with a wavefunction that is very large (a Dirac delta) at a particular position x and zero everywhere else. If one performs a position measurement on such a wavefunction, the result x will be obtained with 100% probability (full certainty). This is called an eigenstate of position (mathematically more precise: a generalized position eigenstate (eigendistribution)). If the particle is in an eigenstate of position then its momentum is completely unknown. On the other hand, if the particle is in an eigenstate of momentum then its position is completely unknown.^[48] In an eigenstate of momentum having a plane wave form, it can be shown that the wavelength is equal to h/p, where h is Planck's constant and p is the momentum of the eigenstate.^[49]

3D confined electron wave functions for each eigenstate in a Quantum Dot. Here, rectangular and triangular-shaped quantum dots are shown. Energy states in rectangular dots are more ‘s-type’ and ‘p-type’. However, in a triangular dot the wave functions are mixed due to confinement symmetry.

Step potential

Main article: Solution of Schrödinger equation for a step potential

The step potential with incident and exiting waves shown.

The potential in this case is given by:

The solutions are superpositions of left and right moving waves:

where the wave vectors are related to the energy via

, and

and the coefficients A and B are determined from the boundary conditions and by imposing a continuous derivative to the solution.

Each term of the solution can be interpreted as an incident, reflected of transmitted component of the wave, allowing the calculation of transmission and reflection coefficients. In contrast to classical mechanics, incident particles with energies higher than the size of the potential step are still partially reflected.

Rectangular potential barrier

Main article: Rectangular potential barrier

This is a model for the quantum tunneling effect, which has important applications to modern devices such as flash memory and the scanning tunneling microscope.

Particle in a box

1-dimensional potential energy box (or infinite potential well)

Main article: Particle in a box

The particle in a 1-dimensional potential energy box is the most simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy inside a certain region and infinite potential energy everywhere outside that region. For the 1-dimensional case in the $x$ direction, the time-independent Schrödinger equation can be written as:^[50]

Writing the differential operator

the previous equation can be seen to be evocative of the classic analogue

with $E$ as the energy for the state $ψ$ , in this case coinciding with the kinetic energy of the particle.

The general solutions of the Schrödinger equation for the particle in a box are:

or, from Euler's formula,

The presence of the walls of the box determines the values of C, D, and k. At each wall (x = 0 and x = L), ψ = 0. Thus when x = 0,

and so D = 0. When x = L,

C cannot be zero, since this would conflict with the Born interpretation. Therefore sin kL = 0, and so it must be that kL is an integer multiple of π. Therefore,

The quantization of energy levels follows from this constraint on k, since

Finite potential well

Main article: Finite potential well

This is generalization of the infinite potential well problem to potential wells of finite depth.

Harmonic oscillator

Main article: Quantum harmonic oscillator

As in the classical case, the potential for the quantum harmonic oscillator is given by:

This problem can be solved either by solving the Schrödinger equation directly, which is not trivial, or by using the more elegant ladder method, first proposed by Paul Dirac. The eigenstates are given by:

- \frac{m\omega x^2}{2 \hbar}} \cdot H_n\left(\sqrt{\frac{m\omega}{\hbar}} x \right), \qquad n = 0,1,2,\ldots. " src="https://highfile.ucoz.com//upload.wikimedia.org/math/1/0/9/109cf0dbdbf920956b79d4adb277d600.png">

where H_n are the Hermite polynomials:

and the corresponding energy levels are

This is another example which illustrates the quantization of energy for bound states.

Physics color pH

pradeep — Wed, 20 Jul 2011 15:56:26 GMT

Red cabbage extract can indicate whether a substance is an acid (like vinegar) or a base (like ammonia). It can also show how strong an acid or a base a substance is. Chemists use the pH scale to express how acidic (like an acid) or basic (like a base) a substance is. A pH value below 7 means that a substance is acidic, and the smaller the number, the more acidic it is. A pH value above 7 means that a substance is basic, and the larger the number, the more basic it is. Red cabbage extract has different colors at different pH values. These colors and approximate pH values are:
approximate pH:

Code

2 4 6 8 10 12
color of extract: red purple violet blue blue-green green

Brith of Physics

pradeep — Wed, 20 Jul 2011 15:35:12 GMT

Physics
From Wikipedia, the free encyclopedia
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This article is about the field of science. For other uses, see Physics (disambiguation).
Physics
E = m c^2\,
Mass–energy equivalence
History of physics
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2-degree-Field Galaxy Redshift Survey
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Bell test · BOOMERanG · Camera obscura experiments · Cavendish experiment · Cosmic Background Explorer (COBE) · Davisson-Germer · Double slit · Foucault pendulum · Franck Hertz · Gravity Probe A · Gravity Probe B · Geiger–Marsden · Homestake experiment · Oil-drop experiment · Michelson-Morley · Neutrino experiment · Sloan Digital Sky Survey · Stern-Gerlach · Wilkinson Microwave Anisotropy Probe
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Physics (from Ancient Greek: φύσις physis "nature") is a natural science that involves the study of matter[1] and its motion through spacetime, along with related concepts such as energy and force.[2] More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.[3][4][5]

Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy.[6] Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 16th century, the natural sciences emerged as unique research programs in their own right.[7] Certain research areas are interdisciplinary, such as biophysics and quantum chemistry, which means that the boundaries of physics are not rigidly defined. In the nineteenth and twentieth centuries physicalism emerged as a major unifying feature of the philosophy of science as physics provides fundamental explanations for every observed natural phenomenon. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening to new research areas in mathematics and philosophy.

Physics is also significant and influential through advances in its understanding that have translated into new technologies. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.