Noncommutative Quantum Mechanics
... Obtain a phase-space formulation of a noncommutative extension of QM in arbitrary number of dimensions; Show that physical previsions are independent of the chosen SW map. ...
... Obtain a phase-space formulation of a noncommutative extension of QM in arbitrary number of dimensions; Show that physical previsions are independent of the chosen SW map. ...
Homework # 5
... probability densities in the range −2λ1 < x < 2λ1 , where λ1 is the de-Broglie wavelength in region 1. (d) What is the penetration depth of the electron in region 2? (e) Next, assume that the particle is an electron with energy E = 1 eV and take V0 = 1.25 eV and |D|2 = 1. Plot the probability densit ...
... probability densities in the range −2λ1 < x < 2λ1 , where λ1 is the de-Broglie wavelength in region 1. (d) What is the penetration depth of the electron in region 2? (e) Next, assume that the particle is an electron with energy E = 1 eV and take V0 = 1.25 eV and |D|2 = 1. Plot the probability densit ...
Hydrogen Atom
... Does this look familiar? It should. It is the same as the energies from the Bohr model. Remember this correctly matched the experimental line spectra for the H-atom. As such, we should hope our new solution also predicts these values. In fact, many would say the QM solution is “exact”. An it is, in ...
... Does this look familiar? It should. It is the same as the energies from the Bohr model. Remember this correctly matched the experimental line spectra for the H-atom. As such, we should hope our new solution also predicts these values. In fact, many would say the QM solution is “exact”. An it is, in ...
Controlling atom motion through the dipole
... Question: How big is Hilbert space? Answer 1: Big Exponential scaling->exact diagonalization difficult Answer 2: Too big Finite range Hamiltonians can’t move states “very far” All eigenstates of such Hamiltonians live on a tiny submanifold of full Hilbert space In 1D, restate as: critical entangleme ...
... Question: How big is Hilbert space? Answer 1: Big Exponential scaling->exact diagonalization difficult Answer 2: Too big Finite range Hamiltonians can’t move states “very far” All eigenstates of such Hamiltonians live on a tiny submanifold of full Hilbert space In 1D, restate as: critical entangleme ...
QCD, Strings and Black holes
... In the sixties many new mesons and hadrons were discovered. It was suggested that these might not be new fundamental particles. Instead they could be viewed as different oscillation modes of a string. ...
... In the sixties many new mesons and hadrons were discovered. It was suggested that these might not be new fundamental particles. Instead they could be viewed as different oscillation modes of a string. ...
slides
... 1 Mass for the Higgson appeared first, as far as I can see, in Higgs’ 66 paper where he gave it mass (a la Mexican hat) by fiat. But it seems the “Mexican Hat” is a figment, an imaginary construct?! 2 I gave a lot of thought to observing the Higgs condensate. I was right in that I could see no way o ...
... 1 Mass for the Higgson appeared first, as far as I can see, in Higgs’ 66 paper where he gave it mass (a la Mexican hat) by fiat. But it seems the “Mexican Hat” is a figment, an imaginary construct?! 2 I gave a lot of thought to observing the Higgs condensate. I was right in that I could see no way o ...
Fixed Points and The Fixed Point Algorithm
... Finding the fixed point for some functions results in a very complicated or impossible equation to solve that would find and exact value for the fixed point. For example if we consider the function f(x)=cos(x) it is apparent from the graph that (or you could prove using the Intermediate Value Theore ...
... Finding the fixed point for some functions results in a very complicated or impossible equation to solve that would find and exact value for the fixed point. For example if we consider the function f(x)=cos(x) it is apparent from the graph that (or you could prove using the Intermediate Value Theore ...
Neils Bohr
... • The Bohr Model of the atom revealed some of the most important properties of molecular and Atomic structure. • The Bohr model gave way to the theory of Atoms, which is called Quantum mechanics. • Model was brought up in 1913. • Electrons orbit around the nucleus which contains the Neutrons and Pro ...
... • The Bohr Model of the atom revealed some of the most important properties of molecular and Atomic structure. • The Bohr model gave way to the theory of Atoms, which is called Quantum mechanics. • Model was brought up in 1913. • Electrons orbit around the nucleus which contains the Neutrons and Pro ...
r interaction * Michael R. Geller
... However, these authors do not explain why the unphysical 1/r 2 interaction is special, apart from the mathematical fact that it permits a separation of the many-particle Schrödinger equation in the hyperradial and hyperangular coordinates employed. Furthermore, the physical nature of the breathing ...
... However, these authors do not explain why the unphysical 1/r 2 interaction is special, apart from the mathematical fact that it permits a separation of the many-particle Schrödinger equation in the hyperradial and hyperangular coordinates employed. Furthermore, the physical nature of the breathing ...
What is Renormalization? G.Peter Lepage
... emphasizing that e0 and m0 are well-defined numbers so long as Λ0 is kept finite; in QED each can be specified to several digits (for any particular value of Λ0 ). Given these “bare” parameters one need know nothing else about renormalization in order to do calculations. One simply computes scatteri ...
... emphasizing that e0 and m0 are well-defined numbers so long as Λ0 is kept finite; in QED each can be specified to several digits (for any particular value of Λ0 ). Given these “bare” parameters one need know nothing else about renormalization in order to do calculations. One simply computes scatteri ...
Lecture 29: Motion in a Central Potential Phy851 Fall 2009
... – We can watch the levels evolve as we increase the perturbation strength, and therefore keep track of the quantum numbers ...
... – We can watch the levels evolve as we increase the perturbation strength, and therefore keep track of the quantum numbers ...
QUANTUM TELEPORTATION
... Two particle quantum system: Neither position nor momentum of either particle is well defined, sum of positions and difference of momenta are precisely defined ...
... Two particle quantum system: Neither position nor momentum of either particle is well defined, sum of positions and difference of momenta are precisely defined ...
PPT
... “Can a quantum mechanical description of physical reality be considered complete?” • Einstein and collaborators (EPR) proposed that by using the conservation laws, one could show that QM was missing something. • Either polarization might occur, but not a mixture, which would violate conservation of ...
... “Can a quantum mechanical description of physical reality be considered complete?” • Einstein and collaborators (EPR) proposed that by using the conservation laws, one could show that QM was missing something. • Either polarization might occur, but not a mixture, which would violate conservation of ...
Classical Models of Subatomic Particles
... that the electron must have a negative rest mass density. While we regard the search for an interior solution to match onto the Kerr-Newman metric as being of interest in its own right, we argue here that assertions concerning the negativity of the rest mass density of the electron (and all other kn ...
... that the electron must have a negative rest mass density. While we regard the search for an interior solution to match onto the Kerr-Newman metric as being of interest in its own right, we argue here that assertions concerning the negativity of the rest mass density of the electron (and all other kn ...
Electric Potential - McMaster Physics and Astronomy
... Bernoulli’s Equation: work and energy in fluids Conditions: steady flow, incompressible fluid. Look at energy balance along a streamline: Change in (kinetic energy/volume) + change in (potential energy/volume) = (net work by pressure)/volume then, or, ...
... Bernoulli’s Equation: work and energy in fluids Conditions: steady flow, incompressible fluid. Look at energy balance along a streamline: Change in (kinetic energy/volume) + change in (potential energy/volume) = (net work by pressure)/volume then, or, ...
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.