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an introductory discussion of the structure of single
an introductory discussion of the structure of single

... defined by either of two lattices [13]. The real space lattice, defined by the basis vectors aˆ1 , aˆ2 , and aˆ3 , is the more obvious of the two, and maps the periodicity of the real structure. In real space, these vectors define the unit cell of graphite. In two dimensions, aˆ1 and aˆ2 define the ...
Rotational Motion and Angular Momentum
Rotational Motion and Angular Momentum

Low-K Dielectrics - Stanford University
Low-K Dielectrics - Stanford University

... • P is related to E through χe the electric susceptibility of the dielectric P = ε oχ e E Therefore D = εo (1+ χe )E = εo κ E where εo is the permittivity of the free space. Note that P also is the density of atomic electric dipole per unit volume P = Σp/V = Np where p is the dipole moment and N is ...
Wave behaviour near critical frequencies in cold bi-ion
Wave behaviour near critical frequencies in cold bi-ion

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... Two blocks of mass m1 = M and m2 = 2M are both sliding towards you on a frictionless surface. The linear momentum of block 1 is half the linear momentum of block 2. You apply the same constant force to both objects in order to bring them to rest. What is the ratio of the two stopping distances d2/d1 ...
Response to Physics Draft by AIP
Response to Physics Draft by AIP

... If a title must be retained, then 'Motion and electricity' is preferable as this describes the content whereas the current title does not. The ending of the first line of text should be changed to ‘… understanding of motion and energy in its mechanical and electrical forms’, because it is not until ...


... impurity in one half and with a pentavalent impurity in the other half. The change carriers in the two regions move about in a random manner and will diffuse from a region of high concentration to a region of low concentration. Thus some of the free electrons from the Nregion diffuse into low concen ...
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Introduction to Mechanics Including Gravity

... The symbol U resembles a potential well or valley. Constant total energy and its decomposition into time-varying kinetic and potential parts are at the core of classical mechanics. Although total energy is always conserved, this particular decomposition is useful only under certain (very important) ...
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CHAPTER 8: Rotational Motion Answers to Questions

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Creating arbitrary quantum vibrational states in a carbon nanotube

... quantum dot (QD) formed in a suspended CNT which lies between two supports (Fig. 1). The QD is controlled by voltages on the electrodes at the ends of the CNT. The resonance frequency of the CNT ωp can be adjusted by the back gates. The strength and the frequency of the electric driving field are de ...
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The quantum spin Hall effect and topological

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... to quantum mechanics, namely the Hamiltonian formalism.3 In the Hamiltonian formulation, the interesting variables are x and its conjugate momentum P. They are the arguments of the Hamilton function H = H(x, P), which is defined on the phase space Γ. Given H, we can define Definition 2.1.1 (Hamilton ...
Nuclear Physics
Nuclear Physics

... atom's angular momentum, or spin. As this direction is random, the beam could be expected to spread into a line. Instead, the beam was split into two parts, depending on whether the atomic spin was oriented up or down. In 1924, Louis de Broglie proposed that all particles behave to an extent like wa ...
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Photon polarization

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photon eigenstates have either right or left circular polarization. A photon that is in a superposition of eigenstates can have linear, circular, or elliptical polarization.The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well, and forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description. The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave. Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.Many of the implications of the mathematical machinery are easily verified experimentally. In fact, many of the experiments can be performed with two pairs (or one broken pair) of polaroid sunglasses.The connection with quantum mechanics is made through the identification of a minimum packet size, called a photon, for energy in the electromagnetic field. The identification is based on the theories of Planck and the interpretation of those theories by Einstein. The correspondence principle then allows the identification of momentum and angular momentum (called spin), as well as energy, with the photon.
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