Limits of fractality: Zeno boxes and relativistic particles
... with the same g and τ that were defined in Eq. (6). This shifts the propagator from an energy expansion to a path expansion, since each term in Eq. (19) can be identified with a classical path. The direct path from y to x, not bouncing off any wall, is the positive n = 0 term in (19). Consider a pat ...
... with the same g and τ that were defined in Eq. (6). This shifts the propagator from an energy expansion to a path expansion, since each term in Eq. (19) can be identified with a classical path. The direct path from y to x, not bouncing off any wall, is the positive n = 0 term in (19). Consider a pat ...
Infinite 1-D Lattice II
... Vn is the (possibly complex) Fourier coefficient of the part of V(x) that looks like a free particle state with wave-vector Kn (momentum ). Note that Kn is larger than the largest k (shortest λ) free particle state that can be supported by a lattice of spacing l. first Brillouin Zone for k ...
... Vn is the (possibly complex) Fourier coefficient of the part of V(x) that looks like a free particle state with wave-vector Kn (momentum ). Note that Kn is larger than the largest k (shortest λ) free particle state that can be supported by a lattice of spacing l. first Brillouin Zone for k ...
Beyond the Cookie Cutter Paradigm
... southward, and after the collision we have, per assumption, two outgoing particles, one heading eastward and one heading westward. To make sense of what happens in this experiment, you need to know that in the quantum world there are no causal links. What takes their place is statistical correlation ...
... southward, and after the collision we have, per assumption, two outgoing particles, one heading eastward and one heading westward. To make sense of what happens in this experiment, you need to know that in the quantum world there are no causal links. What takes their place is statistical correlation ...
Quantum cryptography protocols robust against photon
... states. The new protocol is as robust as BB84 against optimal individual eavesdropping, and is much more robust than BB84 against the most general photon-number splitting attack, increasing the security of QKD implementations that use weak laser pulses. Keywords: Quantum key distribution, implementa ...
... states. The new protocol is as robust as BB84 against optimal individual eavesdropping, and is much more robust than BB84 against the most general photon-number splitting attack, increasing the security of QKD implementations that use weak laser pulses. Keywords: Quantum key distribution, implementa ...
5.2 The Wave Equation
... have wave properties, and we have seen quite a few examples of experimental data that support this claim. Eventually, I am going to have to face the challenge, and come up with some serious mathematical theory to support this claim. If particles have wave properties and can be described by a wave fu ...
... have wave properties, and we have seen quite a few examples of experimental data that support this claim. Eventually, I am going to have to face the challenge, and come up with some serious mathematical theory to support this claim. If particles have wave properties and can be described by a wave fu ...
1. Gravitational Thermodynamics and the Cosmological Constant
... Here it is crucial to address the history of conceiving Einstein’s Equations as purely classical equations, when they should have been conceived as purely quantum equations in which the matter represents the eigenfrequencies of the left hand side gravitational Hamiltonian. From equation (2.23) it is ...
... Here it is crucial to address the history of conceiving Einstein’s Equations as purely classical equations, when they should have been conceived as purely quantum equations in which the matter represents the eigenfrequencies of the left hand side gravitational Hamiltonian. From equation (2.23) it is ...
Atomic Structure
... If a particle of mass m has a definite energy E, its wave function (x, y, z, t) is a product of a time-independent wave function (x, y, z) and a factor that depends on time but not position. Then the probability distribution function |(x, y, z, t)|2 = |(x, y, z)|2 does not depend on time (statio ...
... If a particle of mass m has a definite energy E, its wave function (x, y, z, t) is a product of a time-independent wave function (x, y, z) and a factor that depends on time but not position. Then the probability distribution function |(x, y, z, t)|2 = |(x, y, z)|2 does not depend on time (statio ...
Quantum Information Technology
... .- The blackbody, Planck's law. Wave-corpuscle duality, De Broglie's law. Electron difraction. Energy quantization. Photoelectric effect. Bohr's atom model. .- Schrödinger equation. Probabilistic interpretation of the wave function. Quantum states and entanglement. Unidimensional potentials. The squ ...
... .- The blackbody, Planck's law. Wave-corpuscle duality, De Broglie's law. Electron difraction. Energy quantization. Photoelectric effect. Bohr's atom model. .- Schrödinger equation. Probabilistic interpretation of the wave function. Quantum states and entanglement. Unidimensional potentials. The squ ...
Quantum-to-classical transition for fluctuations in the early Universe
... possessed the unrealistic capabilities of observing, for example, particle numbers instead of field amplitudes, one would never see any effect of coherences between different “classical trajectories” |y(η)i – they represent “consistent histories” [3, 18] to an excellent approximation. The quantum or ...
... possessed the unrealistic capabilities of observing, for example, particle numbers instead of field amplitudes, one would never see any effect of coherences between different “classical trajectories” |y(η)i – they represent “consistent histories” [3, 18] to an excellent approximation. The quantum or ...
Document
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known is ...
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known is ...
CMC Chapter 05
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known is ...
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known is ...
Document
... Ground States and Excited States • When an atom has its electrons in their lowest possible energy levels, it is in its ground state • When an electron has been promoted to a higher level, it is in an excited state ...
... Ground States and Excited States • When an atom has its electrons in their lowest possible energy levels, it is in its ground state • When an electron has been promoted to a higher level, it is in an excited state ...
CMC Chapter 05
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known is ...
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known is ...
C. - Elliott County Schools
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known ...
... • Heisenberg showed it is impossible to take any measurement of an object without disturbing it. • The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time. • The only quantity that can be known ...
Part (a): Matrix Elements
... respectively, and the center of mass energy s = 4E 2 . There are two distinguisable polarization vectors for each photon, namely µ (1) = (0, 1, i, 0) µ (2) = (0, 1, −i, 0) . In order to compute the sum, I will complete the sum for one outgoing photon and then generalize to N outgoing photons. For ...
... respectively, and the center of mass energy s = 4E 2 . There are two distinguisable polarization vectors for each photon, namely µ (1) = (0, 1, i, 0) µ (2) = (0, 1, −i, 0) . In order to compute the sum, I will complete the sum for one outgoing photon and then generalize to N outgoing photons. For ...
Quantum Numbers
... numbers. First, the "primary quantum number," which is given the symbol n, corresponds to those colored rows you saw in the chart. The lowest row, the pink one, has electrons with n=1; the yellow row is n=2, and they go up from there. All right, so n tells you which of the "main" energy levels you' ...
... numbers. First, the "primary quantum number," which is given the symbol n, corresponds to those colored rows you saw in the chart. The lowest row, the pink one, has electrons with n=1; the yellow row is n=2, and they go up from there. All right, so n tells you which of the "main" energy levels you' ...
Natural Nonlinear Quantum Units and Human Artificial Linear
... the natural mass unit µ, the traditional approach with three constants can now be reduced to two constants, i.e. to one length and one time unit connected to the natural mass unit µ. Clearly, the human artificial SI references λu = 1m and u = 1m/s can not have any fundamental physical meaning at all ...
... the natural mass unit µ, the traditional approach with three constants can now be reduced to two constants, i.e. to one length and one time unit connected to the natural mass unit µ. Clearly, the human artificial SI references λu = 1m and u = 1m/s can not have any fundamental physical meaning at all ...
Bohr–Einstein debates
The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr. Their debates are remembered because of their importance to the philosophy of science. An account of the debates was written by Bohr in an article titled ""Discussions with Einsteinon Epistemological Problems in Atomic Physics"". Despite their differences of opinion regarding quantum mechanics, Bohr and Einstein had a mutual admiration that was to last the rest of their lives.The debates represent one of the highest points of scientific research in the first half of the twentieth century because it called attention to an element of quantum theory, quantum non-locality, which is absolutely central to our modern understanding of the physical world. The consensus view of professional physicists has been that Bohr proved victorious, and definitively established the fundamental probabilistic character of quantum measurement.