... Abstract A Schrödinger type equation for a mathematical probability amplitude (x, t) is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M and charge e, moving in a potential V (x). The particle phase space probability density is ...
Space-Time Approach to Non-Relativistic Quantum Mechanics
... measurements such as A, 8, C, . might be the succession of measurements of the coordinate x at successive times tt, t2, t3, . , where t;+i = t;+ e. Let the value, which might result from measurement of the coordinate at time t;, be x;. Thus, if A is a measurement of x at t~ then x~ is what we previo ...
... measurements such as A, 8, C, . might be the succession of measurements of the coordinate x at successive times tt, t2, t3, . , where t;+i = t;+ e. Let the value, which might result from measurement of the coordinate at time t;, be x;. Thus, if A is a measurement of x at t~ then x~ is what we previo ...
Homework 8
... i) For E > V0 , incident particles can be reflected as well as transmitted; and ii) For 0 < E < V0 , there is an exponentially decaying probability of observing a particle in the classically forbidden region. We can explore these effects further by changing the step into a barrier, i.e., we now consid ...
... i) For E > V0 , incident particles can be reflected as well as transmitted; and ii) For 0 < E < V0 , there is an exponentially decaying probability of observing a particle in the classically forbidden region. We can explore these effects further by changing the step into a barrier, i.e., we now consid ...
Long-Range Correlations in the Nonequilibrium Quantum Relaxation of a Spin... V 85, N 15
... Nonequilibrium dynamical properties of quantum systems have been of interest recently, experimentally and theoretically. Measurements on magnetic relaxation at low temperatures show deviations from the classical exponential decay [1], which was explained by the effect of quantum tunneling. On the th ...
... Nonequilibrium dynamical properties of quantum systems have been of interest recently, experimentally and theoretically. Measurements on magnetic relaxation at low temperatures show deviations from the classical exponential decay [1], which was explained by the effect of quantum tunneling. On the th ...
An Introduction to Quantum Control
... where N is a ∗-algebra of operators on a finite-dimensional Hilbert space and P is a state on N , is called a (finite-dimensional) quantum probability space. A ∗-algebra N is a vector space with multiplication and involution (e.g. B(H)). A linear map P : N → C that is positive (P(A) ≥ 0 if A ≥ 0) an ...
... where N is a ∗-algebra of operators on a finite-dimensional Hilbert space and P is a state on N , is called a (finite-dimensional) quantum probability space. A ∗-algebra N is a vector space with multiplication and involution (e.g. B(H)). A linear map P : N → C that is positive (P(A) ≥ 0 if A ≥ 0) an ...
Chapter 40 Problems
... angle does the recoiling electron have kinetic energy equal to the energy of the scattered photon? 24. A 0.110-nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backward. Find the momentum and the kinetic energy of the electron. 25. ...
... angle does the recoiling electron have kinetic energy equal to the energy of the scattered photon? 24. A 0.110-nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backward. Find the momentum and the kinetic energy of the electron. 25. ...
Near field heat transfer between metamaterials
... Wien wavelength ( T c /( k B T) ), energy radiative transfer is maximal when both media behave like blackbodies [2]. In this situation, the transfer is driven by the famous Stefan-Boltzmann law and exchanges only depends on the difference of media temperatures power four. When two bodies a ...
... Wien wavelength ( T c /( k B T) ), energy radiative transfer is maximal when both media behave like blackbodies [2]. In this situation, the transfer is driven by the famous Stefan-Boltzmann law and exchanges only depends on the difference of media temperatures power four. When two bodies a ...
Exploring a Classical Model of the Helium Atom
... trivial symmetry, which turned out to be unstable. As for the correct understanding of quantum-classical correspondence, we had to wait for the work by Gutzwiller, 5) - 7) which shows that all periodic orbits (i.e., including nontrivial ones) have to be taken into account to obtain energy level spac ...
... trivial symmetry, which turned out to be unstable. As for the correct understanding of quantum-classical correspondence, we had to wait for the work by Gutzwiller, 5) - 7) which shows that all periodic orbits (i.e., including nontrivial ones) have to be taken into account to obtain energy level spac ...
Chapter 2 Atomic Motion in an Optical Standing Wave
... where m is the atomic mass, kL is the wave number of the laser light, and the potential amplitude V0 is proportional to the laser intensity and inversely proportional to the detuning from the nearest atomic resonance (which in these experiments is one of the components of the cesium D2 spectral line ...
... where m is the atomic mass, kL is the wave number of the laser light, and the potential amplitude V0 is proportional to the laser intensity and inversely proportional to the detuning from the nearest atomic resonance (which in these experiments is one of the components of the cesium D2 spectral line ...
Miguel Lorente - International Society for the Advanced Study of
... spacetime is reduced to QM of simple alternatives. Logically from the principles of QM the structure of spacetime emerges as a derived concepts. LONERGAN [11] has developed a philosophical interpretation of the structure of spacetime, using the teory of emergent probability as immanent form for the ...
... spacetime is reduced to QM of simple alternatives. Logically from the principles of QM the structure of spacetime emerges as a derived concepts. LONERGAN [11] has developed a philosophical interpretation of the structure of spacetime, using the teory of emergent probability as immanent form for the ...
Main
... Introduction.– Deutsch’s algorithm is not only the first quantum algorithm but also one of the simplest [1]. Although the algorithm was working probabilistically in its original form, it has not been difficult to improve it to a deterministic one [2, 3]. The Deutsch algorithm involves two qubits and ...
... Introduction.– Deutsch’s algorithm is not only the first quantum algorithm but also one of the simplest [1]. Although the algorithm was working probabilistically in its original form, it has not been difficult to improve it to a deterministic one [2, 3]. The Deutsch algorithm involves two qubits and ...
Book Review: It Must Be Beautiful: Great Equations of Modern
... of gauge invariance could indeed specify the behavior of a fundamental force.” The Yang-Mills principle can be summarized in a slogan: force is curvature. Curvature is associated with surfaces. It represents the turning or rotating that takes place when some object is transported around the closed ...
... of gauge invariance could indeed specify the behavior of a fundamental force.” The Yang-Mills principle can be summarized in a slogan: force is curvature. Curvature is associated with surfaces. It represents the turning or rotating that takes place when some object is transported around the closed ...
The fractional quantum Hall effect in wide quantum wells
... Figure 1: (a) Color plot of the longitudinal resistance of a two-dimensional electron system in an 80 nm quantum well. In the lower density range the second subband (2SB) of the host quantum well is not yet occupied. When it becomes populated at higher densities, we observe an interplay of quantum H ...
... Figure 1: (a) Color plot of the longitudinal resistance of a two-dimensional electron system in an 80 nm quantum well. In the lower density range the second subband (2SB) of the host quantum well is not yet occupied. When it becomes populated at higher densities, we observe an interplay of quantum H ...
Igcse chemistry lesson 2
... in this specification 1.19 use the state symbols (s), (l), (g) and (aq) in chemical equations to represent solids, liquids, gases and aqueous solutions respectively 1.20 understand how the formulae of simple compounds can be obtained experimentally, including metal oxides, water and salts containing ...
... in this specification 1.19 use the state symbols (s), (l), (g) and (aq) in chemical equations to represent solids, liquids, gases and aqueous solutions respectively 1.20 understand how the formulae of simple compounds can be obtained experimentally, including metal oxides, water and salts containing ...
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the elemental (baryonic) mass of the universe.In everyday life on Earth, isolated hydrogen atoms (usually called ""atomic hydrogen"" or, more precisely, ""monatomic hydrogen"") are extremely rare. Instead, hydrogen tends to combine with other atoms in compounds, or with itself to form ordinary (diatomic) hydrogen gas, H2. ""Atomic hydrogen"" and ""hydrogen atom"" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen (which would refer to isolated hydrogen atoms).