Cosmology Prof. Yves Gaspar COURSE CONTENT Cosmology
... evolution of the universe. In this field, various disciplines of physics, which are usually taught separately, are used in a unified framework. The course also contains a part dedicated to theoretical astrophysics, which studies the stars and their evolution, the general aim being the study of the p ...
... evolution of the universe. In this field, various disciplines of physics, which are usually taught separately, are used in a unified framework. The course also contains a part dedicated to theoretical astrophysics, which studies the stars and their evolution, the general aim being the study of the p ...
Quantum Theory – Consciousness
... including the physical brain. To some this is heresy. • Complementarity: a single quantum mechanical entity can either behave as a particle or as wave, but never simultaneously as both; that a stronger manifestation of the particle nature leads to a weaker manifestation of the wave nature and vice v ...
... including the physical brain. To some this is heresy. • Complementarity: a single quantum mechanical entity can either behave as a particle or as wave, but never simultaneously as both; that a stronger manifestation of the particle nature leads to a weaker manifestation of the wave nature and vice v ...
ASSIGNMENTS Week 6 (F. Saueressig) Cosmology 14/15 (NWI
... When Einstein studied the cosmological implications of his equations, he was guided by the idea that the universe should be spatially finite and static. In order to realize this idea he had to introduce the cosmological constant Λ. Following his path, consider a closed (k = +1) FRW model containing ...
... When Einstein studied the cosmological implications of his equations, he was guided by the idea that the universe should be spatially finite and static. In order to realize this idea he had to introduce the cosmological constant Λ. Following his path, consider a closed (k = +1) FRW model containing ...
Exercises #3
... •Problem 1. Plot the first Bessel function J0 (x) in the interval {0, 10}. Find the location of the zeros. •Problem 2. The Legendre polynomials (which arise in quantum mechanics en route to the spherical harmonics) satisfy the relation (n + 1)Pn+1 (x) = (2n + 1)xPn (x) − nPn−1 (x), with P0 (x) = 1 a ...
... •Problem 1. Plot the first Bessel function J0 (x) in the interval {0, 10}. Find the location of the zeros. •Problem 2. The Legendre polynomials (which arise in quantum mechanics en route to the spherical harmonics) satisfy the relation (n + 1)Pn+1 (x) = (2n + 1)xPn (x) − nPn−1 (x), with P0 (x) = 1 a ...
슬라이드 1
... Hamiltonian operator energy & wavefunction (solving a partial differential equation) with ...
... Hamiltonian operator energy & wavefunction (solving a partial differential equation) with ...
Symmetry: a bridge between nature and culture
... doubt find it more convenient to create a geometry different from ours, and better adapted to their impressions; but as for us, in the presence of the same impressions, it is certain that we should not find it more convenient to make a change. (Poincaré, 1895, Conclusions) In fact, with Galileo Gali ...
... doubt find it more convenient to create a geometry different from ours, and better adapted to their impressions; but as for us, in the presence of the same impressions, it is certain that we should not find it more convenient to make a change. (Poincaré, 1895, Conclusions) In fact, with Galileo Gali ...
Emergence of Modern Science
... The foundations of quantum mechanics were established during the first half of the twentieth century by Werner Heisenberg, Max Planck, Louis de Broglie, Albert Einstein, Niels Bohr, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli and others. ...
... The foundations of quantum mechanics were established during the first half of the twentieth century by Werner Heisenberg, Max Planck, Louis de Broglie, Albert Einstein, Niels Bohr, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli and others. ...
QUANTUM CHEMISTRY AND GROUP THEORY(2) M.Sc. DEGREE
... be expressed as Ψ (x, y, z, t) for a particle in 3D box. The probability of finding a particle in the volume element dτ is Ψ *(x, y, z, t) Ψ (x, y, z, t) dτ at time t. The wave function must satisfy certain mathematical conditions because of this probabilistic interpretation. For the case of a singl ...
... be expressed as Ψ (x, y, z, t) for a particle in 3D box. The probability of finding a particle in the volume element dτ is Ψ *(x, y, z, t) Ψ (x, y, z, t) dτ at time t. The wave function must satisfy certain mathematical conditions because of this probabilistic interpretation. For the case of a singl ...
Localization, interaction and the modern interpretation(s) of quantum mechanics
... physicists to speculate that it may be precisely an incomplete understanding of quantum physics which is a root cause of the problem. And there is indeed a renewed wider interest in such fundamental approaches: recent developments include physical axioms for quantum theory, new formalisms without ba ...
... physicists to speculate that it may be precisely an incomplete understanding of quantum physics which is a root cause of the problem. And there is indeed a renewed wider interest in such fundamental approaches: recent developments include physical axioms for quantum theory, new formalisms without ba ...
Homework 5 { PHYS 5450
... (c) Make a graphical representation of the momentum probability densities for n = 1 and n = 2. (d) Sketch the momentum probability densities for a large value of n. (e) Using n(p) evaluate the expectation value of the momentum p (f) Using n(p) write the expectation vale of p2 as an integral you ...
... (c) Make a graphical representation of the momentum probability densities for n = 1 and n = 2. (d) Sketch the momentum probability densities for a large value of n. (e) Using n(p) evaluate the expectation value of the momentum p (f) Using n(p) write the expectation vale of p2 as an integral you ...
Renormalization group
In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.