Vibrational motion
... • Mathematical reason: v cannot take negative values, for if it did the wavefunction would be illbehaved. • Physical reason (same as the particle in a square well): the particle is confined, its position not completely uncertain, and its momentum and kinetic energy cannot be exactly zero. • The zero ...
... • Mathematical reason: v cannot take negative values, for if it did the wavefunction would be illbehaved. • Physical reason (same as the particle in a square well): the particle is confined, its position not completely uncertain, and its momentum and kinetic energy cannot be exactly zero. • The zero ...
Space-time fractional derivative operators
... width grows like the square root of time. Anomalous diffusion occurs when the growth rate or the shape of the particle distribution is different than the classical model predicts. Anomalous diffusion is observed in many physical situations, motivating the development of new mathematical and physical ...
... width grows like the square root of time. Anomalous diffusion occurs when the growth rate or the shape of the particle distribution is different than the classical model predicts. Anomalous diffusion is observed in many physical situations, motivating the development of new mathematical and physical ...
Metric fluctuations and the weak equivalence principle
... fluctuations of spacetime geometry were analysed stemming from quantum fluctuations of matter fields in the context of a semiclassical theory of gravity. This leads to a stochastic behaviour of the metric tensor. Furthermore the effects of fluctuations of spacetime geometry leading to, e.g., lightco ...
... fluctuations of spacetime geometry were analysed stemming from quantum fluctuations of matter fields in the context of a semiclassical theory of gravity. This leads to a stochastic behaviour of the metric tensor. Furthermore the effects of fluctuations of spacetime geometry leading to, e.g., lightco ...
Full-Text PDF
... Paul A. M. Dirac devoted much of his life-long efforts to the task of making quantum mechanics compatible with special relativity. Harmonic oscillators serve as an instrument for illustrating quantum mechanics, while special relativity is the physics of the Lorentz group. Thus, Dirac attempted to co ...
... Paul A. M. Dirac devoted much of his life-long efforts to the task of making quantum mechanics compatible with special relativity. Harmonic oscillators serve as an instrument for illustrating quantum mechanics, while special relativity is the physics of the Lorentz group. Thus, Dirac attempted to co ...
What is quantum unique ergodicity?
... extremely strong condition — the existence of a single periodic orbit is enough to show that classical unique ergodicity fails. On the other hand, quantum mechanics is not expected to be so sensitive to individual orbits. Since quantum particles are somehow ‘smeared out’, the behaviour of a quantum ...
... extremely strong condition — the existence of a single periodic orbit is enough to show that classical unique ergodicity fails. On the other hand, quantum mechanics is not expected to be so sensitive to individual orbits. Since quantum particles are somehow ‘smeared out’, the behaviour of a quantum ...
- Philsci
... find in the same way that the transformation qi´ = aiqi + bi(t) is a symmetry of the Hamiltonian. That means that the position-value of each individual particle can be linearly transformed in its own independent way, without any change in the form of the dynamics. However, if we now introduce an int ...
... find in the same way that the transformation qi´ = aiqi + bi(t) is a symmetry of the Hamiltonian. That means that the position-value of each individual particle can be linearly transformed in its own independent way, without any change in the form of the dynamics. However, if we now introduce an int ...
Notes for Lecture 2 Miller Indices, Quantum Mechanics
... As an exercise, figure out the Miller indices of the lattice lines for the left diagram. In the middle diagram, indicate lattice lines with Miller indices (1̄1). In the right ...
... As an exercise, figure out the Miller indices of the lattice lines for the left diagram. In the middle diagram, indicate lattice lines with Miller indices (1̄1). In the right ...
Quantum and Ecosystem Entropies
... scaling, along with the general issue of appropriateness of allometric equations in biology, are topics of lively discussion in the literature. Two recent papers illustrate some of the relevant issues. In an exhaustive re-analysis of earlier data, Dodds et al. (2001) rejected a quarter-power scaling ...
... scaling, along with the general issue of appropriateness of allometric equations in biology, are topics of lively discussion in the literature. Two recent papers illustrate some of the relevant issues. In an exhaustive re-analysis of earlier data, Dodds et al. (2001) rejected a quarter-power scaling ...
Direct Characterization of Quantum Dynamics
... values of the stabilizer and normalizer operators, can also be performed in a temporal sequence on the same pair of qubits with only one Bell-state generation. This is because at the end of each measurement, the output state is in fact in one of the four possible Bell states, which can be utilized a ...
... values of the stabilizer and normalizer operators, can also be performed in a temporal sequence on the same pair of qubits with only one Bell-state generation. This is because at the end of each measurement, the output state is in fact in one of the four possible Bell states, which can be utilized a ...
Pre-Calculus 12A Section 7.3 Solving Exponential Equations
... Since both sides are single powers with the same base, the exponents must be equal. Equate the exponents and solve: ...
... Since both sides are single powers with the same base, the exponents must be equal. Equate the exponents and solve: ...
Document
... system, the [distant] second system may be left in states with two different [types of] wavefunctions.” • 1935 Schrödinger’s entanglement = nonseparability. “Maximal knowledge of a total system does not necessarily include total knowledge of all its parts, not even when these are fully separated fro ...
... system, the [distant] second system may be left in states with two different [types of] wavefunctions.” • 1935 Schrödinger’s entanglement = nonseparability. “Maximal knowledge of a total system does not necessarily include total knowledge of all its parts, not even when these are fully separated fro ...
An amusing analogy: modelling quantum
... and interact with a younger copy of itself in a consistent way. Figure 1(a) shows a 2D wormhole embedded in a fictitious 3D space. (The same wormhole can equivalently be represented as in figure 1(b).) In the following, we will limit ourselves to the simpler situation where the sizes of the wormhole ...
... and interact with a younger copy of itself in a consistent way. Figure 1(a) shows a 2D wormhole embedded in a fictitious 3D space. (The same wormhole can equivalently be represented as in figure 1(b).) In the following, we will limit ourselves to the simpler situation where the sizes of the wormhole ...
Rigid Rotations
... to do with quantum mechanics – after all there is nothing quantum mechanical about the box drawn above – but has everything to do with geometry. Thus, we will find that, while linear momentum operators commute with one another ( pˆ x pˆ y = pˆ y pˆ x ) the same will not be true for angular momenta b ...
... to do with quantum mechanics – after all there is nothing quantum mechanical about the box drawn above – but has everything to do with geometry. Thus, we will find that, while linear momentum operators commute with one another ( pˆ x pˆ y = pˆ y pˆ x ) the same will not be true for angular momenta b ...