Quantum Mechanics - Home Page for Richard Fitzpatrick
... The above expression is called the normalization condition, and must be satisfied by any complete set of probabilities. This condition is equivalent to the self-evident statement that an observation of a system must definitely result in one of its possible outcomes. There is another way in which we ...
... The above expression is called the normalization condition, and must be satisfied by any complete set of probabilities. This condition is equivalent to the self-evident statement that an observation of a system must definitely result in one of its possible outcomes. There is another way in which we ...
Electronic structures of „In,Ga…As/GaAs quantum dot molecules
... 共200⫻ 30 Å2兲 self-assembled QDM’s. So far, most experiments on self-assembled QDM’s are optical3 and most theories are based on continuum models, such as effective mass approximations.3 These simple models ignore or drastically simplify important real material properties such as strain, atomistic sy ...
... 共200⫻ 30 Å2兲 self-assembled QDM’s. So far, most experiments on self-assembled QDM’s are optical3 and most theories are based on continuum models, such as effective mass approximations.3 These simple models ignore or drastically simplify important real material properties such as strain, atomistic sy ...
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation Dorit Aharonov
... Our main result clarifies the picture. We show: Theorem 1. The model of adiabatic computation with local Hamiltonians involving three qubit interactions is polynomially equivalent to the standard model of quantum computation. This shows that universal quantum computation can be fully studied and imp ...
... Our main result clarifies the picture. We show: Theorem 1. The model of adiabatic computation with local Hamiltonians involving three qubit interactions is polynomially equivalent to the standard model of quantum computation. This shows that universal quantum computation can be fully studied and imp ...
Fock Matrix Construction for Large Systems
... This licentiate thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree–Fock calculations. The methods described are also applicable in ...
... This licentiate thesis deals with quantum chemistry methods for large systems. In particular, the thesis focuses on the efficient construction of the Coulomb and exchange matrices which are important parts of the Fock matrix in Hartree–Fock calculations. The methods described are also applicable in ...
Experimental Investigations in Introductory Physics
... also are in contrast to the discipline of mathematics. A mathematical system or theory can be created and it need only be self-consistent. This is, of course, necessary but not sufficient for a physical law. A brief history of the quark theory, which was advanced independently in 1963 by Murray Gell ...
... also are in contrast to the discipline of mathematics. A mathematical system or theory can be created and it need only be self-consistent. This is, of course, necessary but not sufficient for a physical law. A brief history of the quark theory, which was advanced independently in 1963 by Murray Gell ...
Realization of an Optomechanical Interface
... tensile stress due to thermal expansion of the membrane, which is locally heated by the lattice laser [25]. The mechanical quality factor Q ¼ !m =m ¼ !m =2 of the fundamental mode is determined in ringdown measurements from the 1=e decay time of the initially excited membrane amplitude. We find ...
... tensile stress due to thermal expansion of the membrane, which is locally heated by the lattice laser [25]. The mechanical quality factor Q ¼ !m =m ¼ !m =2 of the fundamental mode is determined in ringdown measurements from the 1=e decay time of the initially excited membrane amplitude. We find ...
Three Dimensional Dirac Semimetal and Quantum Transports in
... as two copies of distinct Weyl fermions. Unfortunately, this expectation is generally not true, because two Weyl nodes with opposite chirality may annihilate each other if they overlap in momentum space, and open up a gap in general. Therefore, additional symmetry is required to protect the 3D Dirac ...
... as two copies of distinct Weyl fermions. Unfortunately, this expectation is generally not true, because two Weyl nodes with opposite chirality may annihilate each other if they overlap in momentum space, and open up a gap in general. Therefore, additional symmetry is required to protect the 3D Dirac ...
Nanoelectromechanical systems
... and gate voltages must exceed the accompanying change in the stored electric field energy due to the redistribution of the charges on the various electrodes (called the ‘charging energy’); the difference between the work done and the charging energy gives the net energy gained by the tunnelling electr ...
... and gate voltages must exceed the accompanying change in the stored electric field energy due to the redistribution of the charges on the various electrodes (called the ‘charging energy’); the difference between the work done and the charging energy gives the net energy gained by the tunnelling electr ...
Hubbard and Kondo lattice models in two dimensions: A QMC study
... calculate time displaced Greens functions more efficiently. The calculation of imaginarytime-displaced correlation functions with the auxiliary-field projector quantum Monte Carlo algorithm provides valuable insight (such as spin and charge gaps) into the model under consideration. Assaad et al. [8] ...
... calculate time displaced Greens functions more efficiently. The calculation of imaginarytime-displaced correlation functions with the auxiliary-field projector quantum Monte Carlo algorithm provides valuable insight (such as spin and charge gaps) into the model under consideration. Assaad et al. [8] ...
Quantum computation with two-electron spins in
... emphasis is on the realistic description of qubit operations, both singlequbit ones and those involving the interaction between neighboring qubits. The decoherence effects are also discussed alongside with certain proposals to alleviate their effects. This thesis is organized as follows. Chapter 2 p ...
... emphasis is on the realistic description of qubit operations, both singlequbit ones and those involving the interaction between neighboring qubits. The decoherence effects are also discussed alongside with certain proposals to alleviate their effects. This thesis is organized as follows. Chapter 2 p ...
Picture - Weebly
... experiences of Copernicus in Poland, Galileo in Italy and later Darwin in England. But science is about constant refinement of theory and its testing procedures. The interpretation of results over many years has in some cases left places in the big picture where there are no dots, because there is n ...
... experiences of Copernicus in Poland, Galileo in Italy and later Darwin in England. But science is about constant refinement of theory and its testing procedures. The interpretation of results over many years has in some cases left places in the big picture where there are no dots, because there is n ...
Particle Spin and the Stern
... The point to be made here is that the spinning object is extended in space, i.e. the spinning sphere example has a non-zero radius. If we try to extend the idea to a point particle by taking the limit of a → 0 we immediately see that the spin angular momentum must vanish unless ω is allowed to be in ...
... The point to be made here is that the spinning object is extended in space, i.e. the spinning sphere example has a non-zero radius. If we try to extend the idea to a point particle by taking the limit of a → 0 we immediately see that the spin angular momentum must vanish unless ω is allowed to be in ...
I am grateful to Mike Weismann for guiding much of this discussion
... at least to Boltzmann (18), and the evolving understanding of quantized states. The early protagonists each had their own ideas, but the orthodox view has common components. Since measurement provided the link between the classical physical world and a quantum mechanical interpretation, a complete ...
... at least to Boltzmann (18), and the evolving understanding of quantized states. The early protagonists each had their own ideas, but the orthodox view has common components. Since measurement provided the link between the classical physical world and a quantum mechanical interpretation, a complete ...
Low-Temperature Phase Diagrams of Quantum Lattice
... the long range order, characterizing the groundstate of HΛ (t), survives at lowtemperatures, with a bound on the critical temperature which depends on t. In Section 5 we also study the less-easy-to-treat phase diagram of the antiferromagnetic regime (J < 0). Further examples are presented in [11]. T ...
... the long range order, characterizing the groundstate of HΛ (t), survives at lowtemperatures, with a bound on the critical temperature which depends on t. In Section 5 we also study the less-easy-to-treat phase diagram of the antiferromagnetic regime (J < 0). Further examples are presented in [11]. T ...
Lecture Notes 01: Conservation Laws: Continuity Equation (Charge Conservation), Poynting's Theorem (Energy Conservation), Poynting's Vector
... n.b. for simplicity’s sake, we have approximated the finite length wire by an ∞-length wire. This will have unphysical, but understandable consequences later on…. ...
... n.b. for simplicity’s sake, we have approximated the finite length wire by an ∞-length wire. This will have unphysical, but understandable consequences later on…. ...
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.