Quantum Galactic Dynamics - The fine structure constant
... of mass µ moving in a spherically symmetric field, centred at position r = 0, can be described by a Schrödinger equation, the last equation at, (3.7) which is just an operator version of (3.1) acting on the state function ψ. The energy E becomes the Hamiltonian operator, (3.8), E = Ĥ = ...
... of mass µ moving in a spherically symmetric field, centred at position r = 0, can be described by a Schrödinger equation, the last equation at, (3.7) which is just an operator version of (3.1) acting on the state function ψ. The energy E becomes the Hamiltonian operator, (3.8), E = Ĥ = ...
Indirect measurement
... nonorthogonal states |ψi and |φi, hψ|φi 6= 0. The best we can do with a projective measurement is use P̂0 = |ψihψ|, P̂1 = Iˆ − P̂0 . In this case, if we get result 1 we know that the system cannot have been in state ψ , since hψ|P̂1 |ψi = 0. So it must have been in state φ. In the case of result 0, ...
... nonorthogonal states |ψi and |φi, hψ|φi 6= 0. The best we can do with a projective measurement is use P̂0 = |ψihψ|, P̂1 = Iˆ − P̂0 . In this case, if we get result 1 we know that the system cannot have been in state ψ , since hψ|P̂1 |ψi = 0. So it must have been in state φ. In the case of result 0, ...
Wave-Particle Duality in the Elastodynamics of the Spacetime
... In this paper, we have examined the nature of the wave-particle duality that comes out of the Elastodynamics of the Spacetime Continuum (STCED). We have noted that deformations propagate in the spacetime continuum by longitudinal (dilatation) and transverse (distortion) wave displacements, which pro ...
... In this paper, we have examined the nature of the wave-particle duality that comes out of the Elastodynamics of the Spacetime Continuum (STCED). We have noted that deformations propagate in the spacetime continuum by longitudinal (dilatation) and transverse (distortion) wave displacements, which pro ...
Semi-classical formula beyond the Ehrenfest time in
... Localized regime: After that time, the coherent state spreads more and more. But its width is still of microscopic size if ∆t 1, i.e. t 12 tE . In more precise terms, the semi-classical measure of ψ (t) is still a Dirac measure at x (t) in that range of time. In our example 21 tE = 3.6. At a tim ...
... Localized regime: After that time, the coherent state spreads more and more. But its width is still of microscopic size if ∆t 1, i.e. t 12 tE . In more precise terms, the semi-classical measure of ψ (t) is still a Dirac measure at x (t) in that range of time. In our example 21 tE = 3.6. At a tim ...
Van der Waals Interaction in QCD
... The aim of this bachelor thesis is to give a description of forces between color singlet hadrons, i.e. colorless hadrons. The interaction treated in this thesis is the strong interaction, with its framework the Quantum Chromodynamics. The study of neutral charged atoms is the equivalent QED process ...
... The aim of this bachelor thesis is to give a description of forces between color singlet hadrons, i.e. colorless hadrons. The interaction treated in this thesis is the strong interaction, with its framework the Quantum Chromodynamics. The study of neutral charged atoms is the equivalent QED process ...
SU(3) Model Description of Be Isotopes
... of Be isotopes with 6 ≤ A ≤ 10 and A = 12, 14, are verified experimentally. For 11 Be and 13 Be nuclei, however, the model predicts ground state spin and parity values of 1/2− and 5/2+ , to be compared with the experimental values of 1/2+ and 1/2− [1], respectively. Low lying spectra of 9 Be, 11 N, ...
... of Be isotopes with 6 ≤ A ≤ 10 and A = 12, 14, are verified experimentally. For 11 Be and 13 Be nuclei, however, the model predicts ground state spin and parity values of 1/2− and 5/2+ , to be compared with the experimental values of 1/2+ and 1/2− [1], respectively. Low lying spectra of 9 Be, 11 N, ...
From Parallel Electric and Magnetic Fields
... has the form of a simple harmonic oscillator (SHO). A QM SHO of this form always has stated quantized energy of the form (2 n + 1) e B, where n is an integer. This yields H2 = pz2 + py2 + (2n + 1 - 2 Sz)e B + m2, with Sz = +1/2 or -1/2. ...
... has the form of a simple harmonic oscillator (SHO). A QM SHO of this form always has stated quantized energy of the form (2 n + 1) e B, where n is an integer. This yields H2 = pz2 + py2 + (2n + 1 - 2 Sz)e B + m2, with Sz = +1/2 or -1/2. ...
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DOCTORAL GENERAL EXAMINATION PART II
... current density is everywhere zero, J⃗ = 0. At t = 0 the sources responsible for the applied magnetic field are turned off. Subse⃗ t) in quently, a current develops in the metal which supports a residual magnetic field B(r, the z-direction. The residual magnetic field inside the cylinder begins with the ...
... current density is everywhere zero, J⃗ = 0. At t = 0 the sources responsible for the applied magnetic field are turned off. Subse⃗ t) in quently, a current develops in the metal which supports a residual magnetic field B(r, the z-direction. The residual magnetic field inside the cylinder begins with the ...
What are we are made of?
... charged W particles and one Z particle. They did not sit well with the light-footed photon. How could the electroweak force, which unifies electromagnetic and weak forces, come about? The Standard Model was threatened. This is where Englert, Brout and Higgs entered the stage with the ingenious mech ...
... charged W particles and one Z particle. They did not sit well with the light-footed photon. How could the electroweak force, which unifies electromagnetic and weak forces, come about? The Standard Model was threatened. This is where Englert, Brout and Higgs entered the stage with the ingenious mech ...
Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen
... and the other half to the kinetic energy of the protons at zero temperature and we can compare with the protonic kinetic energies calculated in Ref. [5]. The zero temperature kinetic energies of the protons obtained is systematically higher than the zero temperature extrapolated results of Ref.[5]. ...
... and the other half to the kinetic energy of the protons at zero temperature and we can compare with the protonic kinetic energies calculated in Ref. [5]. The zero temperature kinetic energies of the protons obtained is systematically higher than the zero temperature extrapolated results of Ref.[5]. ...
On distinguishability, orthogonality, and violations of the second law: contradictory assumptions, contrasting pieces of knowledge
... procedures.5 We do not know which of the two, but we can perform a measurement on the instance and record the outcome. Suppose there exists a measurement procedure such that some (at least one) of its outcomes have vanishing probabilities for the first preparation and non-vanishing probabilities for ...
... procedures.5 We do not know which of the two, but we can perform a measurement on the instance and record the outcome. Suppose there exists a measurement procedure such that some (at least one) of its outcomes have vanishing probabilities for the first preparation and non-vanishing probabilities for ...
Chapter 7 The Schroedinger Equation in One Dimension In classical
... In classical mechanics the state of motion of a particle is specified by the particle’s position and velocity. In quantum mechanics the state of motion of a particle is given by the wave function. The goal is to predict how the state of motion will evolve as time goes by. This is what the equation o ...
... In classical mechanics the state of motion of a particle is specified by the particle’s position and velocity. In quantum mechanics the state of motion of a particle is given by the wave function. The goal is to predict how the state of motion will evolve as time goes by. This is what the equation o ...
4 Group theory and the periodic table of chemical elements
... The idea of first principles (elements) as primary constituents of matter is not new. In this respect, the Greek philosophers of Antiquity are a good starting point without denying that similar ideas could have been developed at other times by other people. For the ancient Greeks, any creation or an ...
... The idea of first principles (elements) as primary constituents of matter is not new. In this respect, the Greek philosophers of Antiquity are a good starting point without denying that similar ideas could have been developed at other times by other people. For the ancient Greeks, any creation or an ...
Spin and orbital Kondo effect in electrostatically coupled quantum dots S. L
... Figure 3a presents the differential conductance of a DQD for ΔE ≠ 0. The high transparency region (VSD, h ≈ 0) corresponds to the spin Kondo effect at the dots (εi+ = εi–, 2*SU(2)). The enhanced conductance in this region, marked by the dark circle, is due to the orbital Kondo effect (ε1+ = ε2– for ...
... Figure 3a presents the differential conductance of a DQD for ΔE ≠ 0. The high transparency region (VSD, h ≈ 0) corresponds to the spin Kondo effect at the dots (εi+ = εi–, 2*SU(2)). The enhanced conductance in this region, marked by the dark circle, is due to the orbital Kondo effect (ε1+ = ε2– for ...