Quantum-classical correspondence in the hydrogen atom in weak
... These high energy states can be described by approximately hydrogenic wave functions with very large principal quantum numbers (n*100) @2,3#. The atoms ~or molecules! in which a valence electron is promoted to such high-n states are generically called ‘‘Rydberg’’ atoms, because the energy levels of ...
... These high energy states can be described by approximately hydrogenic wave functions with very large principal quantum numbers (n*100) @2,3#. The atoms ~or molecules! in which a valence electron is promoted to such high-n states are generically called ‘‘Rydberg’’ atoms, because the energy levels of ...
3.3 The time-dependent Schrödinger equation
... if the potential V is constant in time each of the energy eigenstates n r with eigenenergy En is separately a solution of the time-dependent Schrödinger equation provided we remember to multiply by the right complex exponential factor ...
... if the potential V is constant in time each of the energy eigenstates n r with eigenenergy En is separately a solution of the time-dependent Schrödinger equation provided we remember to multiply by the right complex exponential factor ...
Is there a stable hydrogen atom in higher dimensions?
... According to the analysis of Ehrenfest, see also Ref. 9, there are statements in all papers that in higher dimensions it is not possible to have stable atoms. It is one of our purposes in this paper to show that it is indeed possible to have stable atoms in higher dimensions. The main point is that ...
... According to the analysis of Ehrenfest, see also Ref. 9, there are statements in all papers that in higher dimensions it is not possible to have stable atoms. It is one of our purposes in this paper to show that it is indeed possible to have stable atoms in higher dimensions. The main point is that ...
Slides - Powerpoint - University of Toronto Physics
... • Two particles collide, one of which was initially moving, and the other initially at rest. Is it possible for both particles to be at rest after the collision? [Assume no outside forces act on the particles.] ...
... • Two particles collide, one of which was initially moving, and the other initially at rest. Is it possible for both particles to be at rest after the collision? [Assume no outside forces act on the particles.] ...
Sharp Tunneling Peaks in a Parametric Oscillator: Quantum Resonances Missing
... time ¼ t!sl is i@ ¼ ðg^ þ hÞ. Since h^ is periodic in time, this equation has Floquet solutions ð þ h Þ ¼ expðih =Þ ðÞ. They define the dimensionless quasienergies [h ¼ 2!sl =!F 1]. In the RWA, the fast oscillating term h^ is disregarded. ~ becomes time-independent. The dime ...
... time ¼ t!sl is i@ ¼ ðg^ þ hÞ. Since h^ is periodic in time, this equation has Floquet solutions ð þ h Þ ¼ expðih =Þ ðÞ. They define the dimensionless quasienergies [h ¼ 2!sl =!F 1]. In the RWA, the fast oscillating term h^ is disregarded. ~ becomes time-independent. The dime ...
Noncommutative geometry with applications to quantum physics
... of Quantum Mechanics. Partial unification is obtained by the Standard Model of elementary particles which combines Quantum Theory and Special Relativity within the framework of Quantum Field Theory, in order to obtain a so far coherent description of three of the four known elementary interactions ( ...
... of Quantum Mechanics. Partial unification is obtained by the Standard Model of elementary particles which combines Quantum Theory and Special Relativity within the framework of Quantum Field Theory, in order to obtain a so far coherent description of three of the four known elementary interactions ( ...
Chapter 6 Impulse and Momentum Continued
... Conceptual Example Is the Total Momentum Conserved? Imagine two balls colliding on a billiard table that is friction-free. Use the momentum conservation principle in answering the following questions. (a) Is the total momentum of the two-ball system the same before and after the collision? (b) Answe ...
... Conceptual Example Is the Total Momentum Conserved? Imagine two balls colliding on a billiard table that is friction-free. Use the momentum conservation principle in answering the following questions. (a) Is the total momentum of the two-ball system the same before and after the collision? (b) Answe ...
progress in quantum foundations - Department of Computer Science
... Our scientific theories aim to accurately describe every phenomenon that can possibly occur in the world we live in. However, one can hope that a theory will not only explain all observable occurrences and predict new results, but will also convey an understanding of the inner workings of nature; an ...
... Our scientific theories aim to accurately describe every phenomenon that can possibly occur in the world we live in. However, one can hope that a theory will not only explain all observable occurrences and predict new results, but will also convey an understanding of the inner workings of nature; an ...
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.