The Quantum Hall Effect in Graphene
... In this case, applying the particle exchange operator swaps two of the coordinates and the resulting wavefunction has an eigenvalue of arbitrary phase, α. Applying the exchange operator a second time will swap the two coordinates back to their original position returning the system to its initial wa ...
... In this case, applying the particle exchange operator swaps two of the coordinates and the resulting wavefunction has an eigenvalue of arbitrary phase, α. Applying the exchange operator a second time will swap the two coordinates back to their original position returning the system to its initial wa ...
Like other physical theories, quantum mechanics deals with
... systems, solutions to Newton’s Equation of Motion exist and are unique, and problematic cases are usually solved by appealing to physical intuition (Symon, K. R., (1960): 23-4). Nevertheless, it is possible to concoct situations in which either the existence or the uniqueness of solutions does not o ...
... systems, solutions to Newton’s Equation of Motion exist and are unique, and problematic cases are usually solved by appealing to physical intuition (Symon, K. R., (1960): 23-4). Nevertheless, it is possible to concoct situations in which either the existence or the uniqueness of solutions does not o ...
The Blind Men and the Quantum
... theories because, while its formalism of has been accepted and used for 80 years, its interpretation remains a matter of controversy and debate. Like the opinions of the 6 blind men, there are many rival QM interpretations on the market. Today we’ll consider three QM interpretations (including mine) ...
... theories because, while its formalism of has been accepted and used for 80 years, its interpretation remains a matter of controversy and debate. Like the opinions of the 6 blind men, there are many rival QM interpretations on the market. Today we’ll consider three QM interpretations (including mine) ...
Unitarity and Effective Field Theory Results in Quantum Gravity
... employing a basis of integral functions, and determining, using that, where the different singularities in the cut go. (Bern, Dixon, Perelstein, ...
... employing a basis of integral functions, and determining, using that, where the different singularities in the cut go. (Bern, Dixon, Perelstein, ...
Self-adjoint operators and solving the Schrödinger equation
... In this tutorial we collect facts from the theory of self-adjoint operators, mostly with a view of what is relevant for applications in mathematical quantum mechanics, in particular for solving the Schrödinger equation. Specific topics include the spectral theorem and functional calculus for self-a ...
... In this tutorial we collect facts from the theory of self-adjoint operators, mostly with a view of what is relevant for applications in mathematical quantum mechanics, in particular for solving the Schrödinger equation. Specific topics include the spectral theorem and functional calculus for self-a ...
x,y - Piazza
... Note that you can’t simply cancel out y on both sides of the second equation, because y may be 0. You should divide into two cases: (i) y = 0; and (2) y , 0. Case (i) gives you two candidate points by substituting y = 0 into the three equation: (x, y) = (3, 0) or (x, y) = (−3, 0). Case (ii) gives λ ...
... Note that you can’t simply cancel out y on both sides of the second equation, because y may be 0. You should divide into two cases: (i) y = 0; and (2) y , 0. Case (i) gives you two candidate points by substituting y = 0 into the three equation: (x, y) = (3, 0) or (x, y) = (−3, 0). Case (ii) gives λ ...
Chapter 3 Symmetry in quantum mechanics
... which is a mathematical expression of the Laporte and Wigner rules allowing radiative transitions to take place only between states of opposite parity. The electric dipole term ~ ·~r. If a Hamiltonian H is invariant under parity, in a multipole expansion is of the form E the non-degenerate states ca ...
... which is a mathematical expression of the Laporte and Wigner rules allowing radiative transitions to take place only between states of opposite parity. The electric dipole term ~ ·~r. If a Hamiltonian H is invariant under parity, in a multipole expansion is of the form E the non-degenerate states ca ...
Electric potential energy
... where we integrate from x0 to x along C2 then backwards from x to x0 along −C1 to form a closed loop. But in the previous section, we showed that all such integrals vanish for the electric field. Therefore, ∆ = 0, and the integral from x0 to x is independent of path. This allows us to define the pot ...
... where we integrate from x0 to x along C2 then backwards from x to x0 along −C1 to form a closed loop. But in the previous section, we showed that all such integrals vanish for the electric field. Therefore, ∆ = 0, and the integral from x0 to x is independent of path. This allows us to define the pot ...
Pair creation
... For F1 only (black line), sudden rise at ω = 2c2, suggests the start of single photon transition By adding F2 (red line), the region ω < 2c 2 is no longer forbidden, due to single photon transition and ...
... For F1 only (black line), sudden rise at ω = 2c2, suggests the start of single photon transition By adding F2 (red line), the region ω < 2c 2 is no longer forbidden, due to single photon transition and ...
Lecture 5
... Every quantum circuit with m gates and n+s can be simulated by a deterministic circuit of size m¢2O(n+s) This implies that at most exponential speedups are possible Uniformity is preseved by the simulation Idea: store the global quantum state on n+s qubits explicitly (with limited precision), apply ...
... Every quantum circuit with m gates and n+s can be simulated by a deterministic circuit of size m¢2O(n+s) This implies that at most exponential speedups are possible Uniformity is preseved by the simulation Idea: store the global quantum state on n+s qubits explicitly (with limited precision), apply ...
3D simulation of a silicon quantum dot in
... The many body Schrödinger equation is solved with CSDFT, using the local density approximation and the effective mass approximation with parabolic bands. CSDFT allows one to fully take into account the effect of magnetic field and spin, and is strictly applicable only to the calculation of ground s ...
... The many body Schrödinger equation is solved with CSDFT, using the local density approximation and the effective mass approximation with parabolic bands. CSDFT allows one to fully take into account the effect of magnetic field and spin, and is strictly applicable only to the calculation of ground s ...
Part I
... • The connection to the macroscopic entropy function S is through the microscopic parameter Ω, which, as we already know, is the number of microstates in a given macrostate. • The connection between them, as discussed in previous chapters, is ...
... • The connection to the macroscopic entropy function S is through the microscopic parameter Ω, which, as we already know, is the number of microstates in a given macrostate. • The connection between them, as discussed in previous chapters, is ...
7th Workshop on Quantum Chaos and Localisation Phenomena
... students and postdocs. During the meeting 18 invited lectures and 5 posters were presented. The presentations were focused on the following topics: quantum chaos and non-linear classical systems, quantum and microwave graphs and billiards, atoms in strong electromagnetic fields, Anderson localisatio ...
... students and postdocs. During the meeting 18 invited lectures and 5 posters were presented. The presentations were focused on the following topics: quantum chaos and non-linear classical systems, quantum and microwave graphs and billiards, atoms in strong electromagnetic fields, Anderson localisatio ...
Photon localizability - Current research interest: photon position
... confusing, in part because there are really 3 problems: 1) For any quantum particle ψ~e-iwt with +ve w= c k k and localizability is limited by FT theorems. 2) If all k's are equally weighted to localize the number probability density, then energy density (and fields in the case of photons) are not ...
... confusing, in part because there are really 3 problems: 1) For any quantum particle ψ~e-iwt with +ve w= c k k and localizability is limited by FT theorems. 2) If all k's are equally weighted to localize the number probability density, then energy density (and fields in the case of photons) are not ...