Part I
... • While classical mechanics regards p and V as functions of time and spatial position, quantum mechanics regards p and V as mathematical operators that create the right differential equation for the problem at hand • In one dimension, the translational momentum operator is ...
... • While classical mechanics regards p and V as functions of time and spatial position, quantum mechanics regards p and V as mathematical operators that create the right differential equation for the problem at hand • In one dimension, the translational momentum operator is ...
Electronic Structure According to the Orbital Approximation
... determinant can be associated to the electron configuration including exactly the same orbitals. This is not necessary valid vice versa, since the same electron configuration with partially occupied np orbitals can be associated to several Slater determinants. In such cases it is not apparent, which S ...
... determinant can be associated to the electron configuration including exactly the same orbitals. This is not necessary valid vice versa, since the same electron configuration with partially occupied np orbitals can be associated to several Slater determinants. In such cases it is not apparent, which S ...
Pairing in a system of a few attractive fermions in a harmonic trap
... function of the distance x. At small distances the offdiagonal correlation is large and practically constant indicating a two-particle coherence. However, at distances comparable to the size of the correlated pair (compare fig. 3) the off-diagonal correlation falls down as expected, i.e. according to ...
... function of the distance x. At small distances the offdiagonal correlation is large and practically constant indicating a two-particle coherence. However, at distances comparable to the size of the correlated pair (compare fig. 3) the off-diagonal correlation falls down as expected, i.e. according to ...
THE QUArtTIC-QUADRATIC OSCILLATOR
... normally expected to involve overcoming an energy barrier. A one-dimensional section through the molecular potential ...
... normally expected to involve overcoming an energy barrier. A one-dimensional section through the molecular potential ...
Quantum centipedes with strong global constraint
... allows the centipede to move is s = 2. The classical dynamics of a centipede with this local constraint has been studied in [2], where the diffusion coefficient of the centipede is worked out as a function of the number of legs. Quantum walks, on the other hand [3, 4, 5, 6], yield ballistic rather t ...
... allows the centipede to move is s = 2. The classical dynamics of a centipede with this local constraint has been studied in [2], where the diffusion coefficient of the centipede is worked out as a function of the number of legs. Quantum walks, on the other hand [3, 4, 5, 6], yield ballistic rather t ...
Hamiltonians Defined as Quadratic Forms
... Remarks. 1. There exist VeR with D(V)nD(H0) = {0}. Thus, while the Hamiltonian operator we have defined is an extension of the operator sum, it may be defined on a much larger domain! 2. D(H) can be described explicitly. Let φ e Q(H^}. It is not hard to prove — Δφ and Vφ both make sense as distribut ...
... Remarks. 1. There exist VeR with D(V)nD(H0) = {0}. Thus, while the Hamiltonian operator we have defined is an extension of the operator sum, it may be defined on a much larger domain! 2. D(H) can be described explicitly. Let φ e Q(H^}. It is not hard to prove — Δφ and Vφ both make sense as distribut ...
Physics 214 Lecture 8
... y(x) must be continuous, with finite dy/dx. dy/dx is related to the momentum. In regions with finite potential, d2y/dx2 must be finite. To avoid infinite energies. This also means that dy/dx must be continuous. There is no significance to the overall sign of y(x). It goes away when we take the absol ...
... y(x) must be continuous, with finite dy/dx. dy/dx is related to the momentum. In regions with finite potential, d2y/dx2 must be finite. To avoid infinite energies. This also means that dy/dx must be continuous. There is no significance to the overall sign of y(x). It goes away when we take the absol ...
Black Hole Evaporation Rates without Spacetime
... a result identical to the generic form of Eq. (1) [21]. In a sense then, black holes are not ideal but ‘‘real black bodies’’ that satisfy conservation laws, result in a nonthermal spectrum, and preserve thermodynamic entropy. In contrast, treated as ideal black bodies, black hole evaporation would l ...
... a result identical to the generic form of Eq. (1) [21]. In a sense then, black holes are not ideal but ‘‘real black bodies’’ that satisfy conservation laws, result in a nonthermal spectrum, and preserve thermodynamic entropy. In contrast, treated as ideal black bodies, black hole evaporation would l ...
Recurrence spectroscopy of atoms in electric fields: Scattering in the...
... We can now write the scattering series, Eq. ~9!, and symbolically replace R nk by R nk,unif wherever there is a bifurcation. In practice, it is easier to extract the s, p, and d components of the scattered wave by interchanging the order of summation and integration in Eq. ~19!. In the electric fiel ...
... We can now write the scattering series, Eq. ~9!, and symbolically replace R nk by R nk,unif wherever there is a bifurcation. In practice, it is easier to extract the s, p, and d components of the scattered wave by interchanging the order of summation and integration in Eq. ~19!. In the electric fiel ...
Statistics of Occupation Numbers
... within the grand canonical ensemble, its distribution is nevertheless extremely sharp for macroscopic systems. Hence, we can generally assume that N and V are determined by external constraints and thereby related the chemical potential directly to the density. In this notebook we concentrate on the ...
... within the grand canonical ensemble, its distribution is nevertheless extremely sharp for macroscopic systems. Hence, we can generally assume that N and V are determined by external constraints and thereby related the chemical potential directly to the density. In this notebook we concentrate on the ...
Statistical mechanics - University of Guelph Physics
... equally well in the opposite direction (from state B to state A), without introducing any other changes in the thermodynamic system or its surroundings. As an example of a reversible transformation, consider the quasi-static compression of a gas. The work done on during the compression can be extrac ...
... equally well in the opposite direction (from state B to state A), without introducing any other changes in the thermodynamic system or its surroundings. As an example of a reversible transformation, consider the quasi-static compression of a gas. The work done on during the compression can be extrac ...
Quantum walk search on satisfiability problems random
... Problems are divided into computational complexity classes generally by the time requirements of their best possible algorithms using big 0 notation. The two main complexity classes used to classify the difficulty of problems are P and NP. These classify problems known as decision problems, those wi ...
... Problems are divided into computational complexity classes generally by the time requirements of their best possible algorithms using big 0 notation. The two main complexity classes used to classify the difficulty of problems are P and NP. These classify problems known as decision problems, those wi ...
Paradox in Wave-Particle Duality
... radial distance from the center of the pattern, x is the position along the horizontal axis, and a and b are constants.(25) Near the center of the interference pattern the term that contains the Bessel function is nearly 1, and the cos2 (bx) term is the dominant factor in the formula. By expanding t ...
... radial distance from the center of the pattern, x is the position along the horizontal axis, and a and b are constants.(25) Near the center of the interference pattern the term that contains the Bessel function is nearly 1, and the cos2 (bx) term is the dominant factor in the formula. By expanding t ...
Shor`s Algorithm for Factorizing Large Integers
... Construct a quantum computer with q 2 = 22 qubits (plus additional qubits for ‘workspace’). The base states are denoted |a, b = |a|b where a, b are binary vectors (i.e. vectors with entries 0,1) of length . Equivalently, a and b (called registers 1 and 2) are integers < q written in binary. At ...
... Construct a quantum computer with q 2 = 22 qubits (plus additional qubits for ‘workspace’). The base states are denoted |a, b = |a|b where a, b are binary vectors (i.e. vectors with entries 0,1) of length . Equivalently, a and b (called registers 1 and 2) are integers < q written in binary. At ...
スライド 1
... Calculation of 11 dim. L-loop amplitude is difficult. By using power counting, however, we can restrict its form. The L-loop amplitude on a torus which includes term will be subdivergences ...
... Calculation of 11 dim. L-loop amplitude is difficult. By using power counting, however, we can restrict its form. The L-loop amplitude on a torus which includes term will be subdivergences ...
104,18415 (2007)
... computation using Abelian and non-Abelian systems. An Abelian anyonic system has two degenerate ground states that cannot mix by a weak local external perturbation in the sense that the errors induced by local perturbations are exponentially suppressed ⬃exp(⫺L/), where L is the linear size of the s ...
... computation using Abelian and non-Abelian systems. An Abelian anyonic system has two degenerate ground states that cannot mix by a weak local external perturbation in the sense that the errors induced by local perturbations are exponentially suppressed ⬃exp(⫺L/), where L is the linear size of the s ...
