Quantum Mechanics: what is it and why is it interesting? Dr. Neil Shenvi
... 1788 – Lagrange’s Mecanique Analytique 1834 – Hamiltonian mechanics 1864 – Maxwell’s equations 1900 – Boltzmann’s entropy equation ...
... 1788 – Lagrange’s Mecanique Analytique 1834 – Hamiltonian mechanics 1864 – Maxwell’s equations 1900 – Boltzmann’s entropy equation ...
Thermal effects on sudden changes and freezing
... dN N 2 N k1 kk 1. For example, in the case of N 2 excitations the Hamiltonian H s in Eq. (1) is decomposed in a state-basis of dimension 1 d2 , i.e., it is a 19 × 19 matrix; for six excitations, H s is represented by a 231 × 231 matrix, and so on. Hence it is evident that for large N th ...
... dN N 2 N k1 kk 1. For example, in the case of N 2 excitations the Hamiltonian H s in Eq. (1) is decomposed in a state-basis of dimension 1 d2 , i.e., it is a 19 × 19 matrix; for six excitations, H s is represented by a 231 × 231 matrix, and so on. Hence it is evident that for large N th ...
A critique of recent semi-classical spin-half quantum plasma theories
... [Eq.(125.7) of [15]], where σ = ± 21 . When T ≫ ~ωce , the quantum number n would be very large, and the tiny spin-dependent correction to the “orbital energy” contributed by the high n term is clearly an insignificant effect. Any semi-classical approach must require n ≫ 1 and thus cannot possibly a ...
... [Eq.(125.7) of [15]], where σ = ± 21 . When T ≫ ~ωce , the quantum number n would be very large, and the tiny spin-dependent correction to the “orbital energy” contributed by the high n term is clearly an insignificant effect. Any semi-classical approach must require n ≫ 1 and thus cannot possibly a ...
Classical limit for quantum mechanical energy eigenfunctions
... the system starting from the Green’s function or the propagator and then reducing its trace to a sum over all periodic orbits1. A general scheme is thus devised to handle the extreme cases of classical dynamics – both integrable and ergodic. With the derivation of ‘trace formula’, the semiclassical ...
... the system starting from the Green’s function or the propagator and then reducing its trace to a sum over all periodic orbits1. A general scheme is thus devised to handle the extreme cases of classical dynamics – both integrable and ergodic. With the derivation of ‘trace formula’, the semiclassical ...
Copyright c 2017 by Robert G. Littlejohn Physics 221B Spring 2017
... that in the quantum theory of the electromagnetic field, measurements of E and B are associated with some operators that act on some ket space, and that these measurements will exhibit statistical fluctuations and obey some uncertainty relations. In the quantum theory of the electromagnetic field, t ...
... that in the quantum theory of the electromagnetic field, measurements of E and B are associated with some operators that act on some ket space, and that these measurements will exhibit statistical fluctuations and obey some uncertainty relations. In the quantum theory of the electromagnetic field, t ...
The general problem of moist processes in ALADIN-2 J.-F
... To start looking at the problem of the micro-physics time-step-length (algorithmically, not scientifically). To prepare testing of deep-convective ideas in a very wide sense (if one wants compatibility between ALARO-10 and ALARO-5 in methods and between AROME and ALARO-5 for micro-physics, cross-fer ...
... To start looking at the problem of the micro-physics time-step-length (algorithmically, not scientifically). To prepare testing of deep-convective ideas in a very wide sense (if one wants compatibility between ALARO-10 and ALARO-5 in methods and between AROME and ALARO-5 for micro-physics, cross-fer ...
Microsoft Word - ANL_form6
... This proposal addresses to one of the foundation stones of modern physics: critical phenomena and phase transitions. Statistical physics is of growing importance in areas ranging from condensed matter physics to cosmology (including problems regarding the origin of the universe itself and of life wi ...
... This proposal addresses to one of the foundation stones of modern physics: critical phenomena and phase transitions. Statistical physics is of growing importance in areas ranging from condensed matter physics to cosmology (including problems regarding the origin of the universe itself and of life wi ...
Angular Momentum
... Conceptual Question 4c Two children are playing with a roll of paper towels. One child holds the roll between the index fingers of her hands so that it is free to rotate, and the second child pulls at constant speed on the free end of the paper towels. As the child pulls the paper towels, the radiu ...
... Conceptual Question 4c Two children are playing with a roll of paper towels. One child holds the roll between the index fingers of her hands so that it is free to rotate, and the second child pulls at constant speed on the free end of the paper towels. As the child pulls the paper towels, the radiu ...
Dimensional Analysis in Engineering
... acceleration is so many metres per second per second, which, when multiplied by t2 which is seconds squared gives metres, as does the other term ut. Thus if somebody copied down the equation wrongly and wrote 12 at (instead of 12 at2 ) then we could surmise that there must be a mistake. This simple ...
... acceleration is so many metres per second per second, which, when multiplied by t2 which is seconds squared gives metres, as does the other term ut. Thus if somebody copied down the equation wrongly and wrote 12 at (instead of 12 at2 ) then we could surmise that there must be a mistake. This simple ...
Quantum Chaos
... What are the appropriate quantum observables to detect the regular or chaotic classical behaviour of the system? More precisely, how does the regular or chaotic classical behaviour translate in the energy levels and eigenstates of the (bound) system? For an open system, in the decay rates, in the ...
... What are the appropriate quantum observables to detect the regular or chaotic classical behaviour of the system? More precisely, how does the regular or chaotic classical behaviour translate in the energy levels and eigenstates of the (bound) system? For an open system, in the decay rates, in the ...
J.J. Thomson and Duhem`s Lagrangian Approaches to
... In the second half of the nineteenth century, the recently emerged thermodynamics underwent a process of mathematisation, and new theoretical frameworks were put forward. Moreover a widespread philosophical and cosmological debate on the second law also emerged. On the specific physical side, two ma ...
... In the second half of the nineteenth century, the recently emerged thermodynamics underwent a process of mathematisation, and new theoretical frameworks were put forward. Moreover a widespread philosophical and cosmological debate on the second law also emerged. On the specific physical side, two ma ...
Quantum Relaxation after a Quench in Systems with Boundaries Ferenc Iglo´i *
... have focused on bulk sites up to now, but all real systems have a finite extent and they are bounded by surfaces and the physical properties in the surface region are considerably different from those in the bulk [18]. Obviously an interesting question is whether the time and length scales character ...
... have focused on bulk sites up to now, but all real systems have a finite extent and they are bounded by surfaces and the physical properties in the surface region are considerably different from those in the bulk [18]. Obviously an interesting question is whether the time and length scales character ...
The origin of the work function
... From the many observations that have been made e.g. by photon spectroscopy and thermo ionic emission [18,19] it is apparent that electrons are bound to a metal by some kind of process. However, the origin of the bonding process is not well understood [18,19]. The work function has been originally in ...
... From the many observations that have been made e.g. by photon spectroscopy and thermo ionic emission [18,19] it is apparent that electrons are bound to a metal by some kind of process. However, the origin of the bonding process is not well understood [18,19]. The work function has been originally in ...
Condensed Matter Physics as a Laboratory for Gravitation and
... The geometric language of General Relativity is not normally related to Condensed Matter (CM) Physics since it is the electromagnetic and not the gravitational interaction that dominates the physics of CM systems. What points in common would then CMP have with Cosmology and the dynamics of objects i ...
... The geometric language of General Relativity is not normally related to Condensed Matter (CM) Physics since it is the electromagnetic and not the gravitational interaction that dominates the physics of CM systems. What points in common would then CMP have with Cosmology and the dynamics of objects i ...
INTRODUCTION TO QUANTUM CHAOS
... thermodynamic limit in which the number of particles tends to infinity. Another branch is an analysis of what the behaviors of linear wave equation solutions may be in a short wavelength or asymptotic limit. It applies equally well in the contexts of quantum mechanics, acoustics, optics, or other li ...
... thermodynamic limit in which the number of particles tends to infinity. Another branch is an analysis of what the behaviors of linear wave equation solutions may be in a short wavelength or asymptotic limit. It applies equally well in the contexts of quantum mechanics, acoustics, optics, or other li ...
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.