string theory.
... special relativity and general relativity are very different, there are many fewer observables in GR. This leads to a contradiction. This is a powerful theorem, but has a hidden assumption that allows for an exception. ...
... special relativity and general relativity are very different, there are many fewer observables in GR. This leads to a contradiction. This is a powerful theorem, but has a hidden assumption that allows for an exception. ...
The Free Particle
... situations. As you will see later, we will usually use the sine-cosine form when dealing with bound states and the exponential form when dealing with scattering states but these rules are not hard and fast. Since the two forms are equivalent, we always try to use the most convenient one at any given ...
... situations. As you will see later, we will usually use the sine-cosine form when dealing with bound states and the exponential form when dealing with scattering states but these rules are not hard and fast. Since the two forms are equivalent, we always try to use the most convenient one at any given ...
Physics 207: Lecture 2 Notes
... Momentum is a Vector (!) quantity x-direction: No net force so Px is conserved. y-direction: Net force, interaction with the ground so depending on the system (i.e., do you include the Earth?) Py is not conserved (system is block and cart only) ...
... Momentum is a Vector (!) quantity x-direction: No net force so Px is conserved. y-direction: Net force, interaction with the ground so depending on the system (i.e., do you include the Earth?) Py is not conserved (system is block and cart only) ...
Atomic 1
... This result was baffling, since there should be 2l + 1 lines on the screen and this result implies that the angular momentum quantum number l should be 1/2, but we know that l can only be an integer. Clearly a problem here. What is going on? in the early 1920’sW. Pauli was the first to suggest that ...
... This result was baffling, since there should be 2l + 1 lines on the screen and this result implies that the angular momentum quantum number l should be 1/2, but we know that l can only be an integer. Clearly a problem here. What is going on? in the early 1920’sW. Pauli was the first to suggest that ...
Equality and Identity and (In)distinguishability in Classical and Quantum Mechanics from the Point of View of Newton's Notion of State
... identical’w.r.t. state properties: All electrons (protons, . . . ) exhibit the same mass at rest, electrical charge, modulus of spin, etc.; Pauli’s exclusion principle: 2 electrons di¤er in at least one quantum number –however: it does not say, which electron is in which state (entanglement); The qu ...
... identical’w.r.t. state properties: All electrons (protons, . . . ) exhibit the same mass at rest, electrical charge, modulus of spin, etc.; Pauli’s exclusion principle: 2 electrons di¤er in at least one quantum number –however: it does not say, which electron is in which state (entanglement); The qu ...
Living in a Quantum World
... These systems are analogous to Schrödinger’s cat. Consider an atom or ion. Its electrons can exist close to the nucleus or farther away—or both at the same time. Such an electron acts like the radioactive atom that has either decayed or not decayed in Schrödinger’s thought experiment. Independently ...
... These systems are analogous to Schrödinger’s cat. Consider an atom or ion. Its electrons can exist close to the nucleus or farther away—or both at the same time. Such an electron acts like the radioactive atom that has either decayed or not decayed in Schrödinger’s thought experiment. Independently ...
o Orbital dipole moments. Orbital precession. Spin-orbit interaction.
... between nucleus and electron. o Instead, must consider magnetic interaction between orbital magnetic moment and the intrinsic spin magnetic moment. o Called spin-orbit interaction. o Weak in one-electron atoms, but strong in multi-electron atoms where total orbital magnetic moment is large. o Co ...
... between nucleus and electron. o Instead, must consider magnetic interaction between orbital magnetic moment and the intrinsic spin magnetic moment. o Called spin-orbit interaction. o Weak in one-electron atoms, but strong in multi-electron atoms where total orbital magnetic moment is large. o Co ...
Chapter 2 Atomic structure and spectra
... where φj (qi ) = Rnj j (ri )Yj mj (θi , ϕi )σmsj represents a spin orbital with σmsj being the spin part of the orbital, either α for msj = 1/2 or β for msj = −1/2 . The electron wave function in Equation (2.16) gives the occupation of the atomic orbitals and represents a given electron configurat ...
... where φj (qi ) = Rnj j (ri )Yj mj (θi , ϕi )σmsj represents a spin orbital with σmsj being the spin part of the orbital, either α for msj = 1/2 or β for msj = −1/2 . The electron wave function in Equation (2.16) gives the occupation of the atomic orbitals and represents a given electron configurat ...
Landau Levels and Quantum Group
... topological Chern-Simons theories [3] as well as in rational conformal field theories and integrable lattice models [4]. Although the abelian ChernSimons theory does not possess a quantum group structure in the literature [3], it might be possible to exhibit one in some other senses. There have been ...
... topological Chern-Simons theories [3] as well as in rational conformal field theories and integrable lattice models [4]. Although the abelian ChernSimons theory does not possess a quantum group structure in the literature [3], it might be possible to exhibit one in some other senses. There have been ...
Probing quantum mechanics towards the everyday world: where do we stand?
... QM. Irrespective of this, it is clear that it is in direct conflict with the QM notion of a superposition of the two states in question, at least so long as we interpret the latter in the way which we were compelled to do at the microlevel. Thus, any confirmation of the predictions of QM based on the ...
... QM. Irrespective of this, it is clear that it is in direct conflict with the QM notion of a superposition of the two states in question, at least so long as we interpret the latter in the way which we were compelled to do at the microlevel. Thus, any confirmation of the predictions of QM based on the ...
The unbreakable code: Is this the lock?
... An even more puzzling feature of entanglement-based quantum cryptography was recently demonstrated here. CQT’s Valerio Scarani, together with European colleagues, showed that the entanglement-based key distribution scheme is far more general and much more powerful than I originally anticipated; it w ...
... An even more puzzling feature of entanglement-based quantum cryptography was recently demonstrated here. CQT’s Valerio Scarani, together with European colleagues, showed that the entanglement-based key distribution scheme is far more general and much more powerful than I originally anticipated; it w ...
sy30_may10_s12
... Proportional to the mass ( m1m2 ) Inversely proportional to the distance (1/r) Circular orbits: Dynamical quantities (v,E,K,U,F) involve radius K(r) = - ½ U(r) Employ conservation of angular momentum in elliptical orbits No need to derive Kepler’s Laws (know the reasons for them) Energy transf ...
... Proportional to the mass ( m1m2 ) Inversely proportional to the distance (1/r) Circular orbits: Dynamical quantities (v,E,K,U,F) involve radius K(r) = - ½ U(r) Employ conservation of angular momentum in elliptical orbits No need to derive Kepler’s Laws (know the reasons for them) Energy transf ...
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.