通过计算氢原子的玻尔半径,加深对量子力学的理解

通过玻尔理论基本假设、不确定关系、薛定谔方程以及波函数性质4种方法求氢原子的玻尔半径,理解了玻尔理论基本假设的半经典、半量子;不确定关系正是微观粒子波动性的必然结果;氢原子中电子遵从薛定谔方程,方程的解析即为波函数,是概率波.     

Copenhagen quantum mechanics

In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists’ laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr’s quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.     

The use of fast field cycling to evaluate the time domain relaxation of starches from tropical fruit seeds

ABSTRACT

A proton NMR relaxation study of the molecular dynamics in flour samples of ‘Eugenia uniflora’ (‘Pitanga’), ’Citrus reticulate’ (‘Tangerine’), ‘Prunus persica’ (‘Peach’), ‘Vitis vinifera’ (‘Grape’), and ‘Cucumis melo’ (‘Honeydew melon’) seeds is presented. The spin–lattice relaxation time was obtained over a broad frequency range from 100?kHz to 100?MHz using both conventional and fast field-cycling NMR techniques. This relaxometry study made possible a comparison between the molecular dynamics behaviour of starch from different fruit seeds and from potatoes. I was possible to conclude that the spin–lattice dispersion presents slightly differences for all samples, in particular at low frequencies. All relaxation dispersions could be well interpreted in terms of power-law relaxation models and domains with different power-law relaxation exponents. For the Peach seeds flour the relaxation dispersion at low frequencies was very similar to that observed for potato’s starch incorporated with 5% organoclay Viscogel B8 nanoparticles.     

Challenges to Bohr’s Wave-Particle Complementarity Principle

Contrary to Bohr’s complementarity principle, in 1995 Rabinowitz proposed that by using entangled particles from the source it would be possible to determine which slit a particle goes through while still preserving the interference pattern in the Young’s two slit experiment. In 2000, Kim et al. used spontaneous parametric down conversion to prepare entangled photons as their source, and almost achieved this. In 2012, Menzel et al. experimentally succeeded in doing this. When the source emits entangled particle pairs, the traversed slit is inferred from measurement of the entangled particle’s location by using triangulation. The violation of complementarity breaches the prevailing probabilistic interpretation of quantum mechanics, and benefits Bohm’s pilot-wave theory.     

Angular distributions of fragments for low-energy photofission induced by linearly polarized photons

The angular distributions of fragments for photofission of even-even nuclei, induced by linearly polarized photons, have been analyzed for the first time within the quantum fission theory, taking into account the deviations of these angular distributions from A. Bohr’s formula.     

Bell’s Theorem: Two Neglected Solutions

Bell’s theorem admits several interpretations or ‘solutions’, the standard interpretation being ‘indeterminism’, a next one ‘nonlocality’. In this article two further solutions are investigated, termed here ‘superdeterminism’ and ‘supercorrelation’. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The latter, supercorrelation, will be studied here by investigating model systems that can mimic it, namely spin lattices. It is shown that in these systems the Bell inequality can be violated, even if they are local according to usual definitions. Violation of the Bell inequality is retraced to violation of ‘measurement independence’. These results emphasize the importance of studying the premises of the Bell inequality in realistic systems.     

Long range and temperature-dependent interaction between an alkali atom and a metallic surface; application to surface ionization

For explaining some long range and temperature dependent charge transfer involved in surface processes dealing with particles leaving a surface, we extend the usual chemisorption theory to larger distances. Treating the interaction of an alkali atom (lithium and sodium) on a metal surface (rhenium) in the chemisorption model, we introduce the temperature in the expression for the effective charges of the adsorbed atom. These effective charges are shown to be very sensitive to the temperature for atom-surface distances larger than 5 Bohr radii. The Coulomb repulsion effect between opposite spin electrons on the adsorbed particle allows us to describe the effective charges of both the positive and negative adsorbed ions. We apply our treatment to the positive surface ionization of thermal particles and give a new expression of the degree of ionization which asymptotically tends to the values of the Saha-Langmuir law. We found that the surface ionization process occurs at distances slightly decreasing with increasing temperatures, which are of the order of 13 Bohr radii for lithium on rhenium and of 15 Bohr radii for sodium on rhenium.     

Paul Ehrenfest, Niels Bohr, and Albert Einstein: Colleagues and Friends

In May 1918 Paul Ehrenfest received a monograph from Niels Bohr in which Bohr had used Ehrenfest’s adiabatic principle as an essential assumption for understanding atomic structure. Ehrenfest responded by inviting Bohr, whom he had never met, to give a talk at a meeting in Leiden in late April 1919, which Bohr accepted; he lived with Ehrenfest, his mathematician wife Tatyana, and their young family for two weeks. Albert Einstein was unable to attend this meeting, but in October 1919 he visited his old friend Ehrenfest and his family in Leiden, where Ehrenfest told him how much he had enjoyed and profited from Bohr’s visit. Einstein first met Bohr when Bohr gave a lecture in Berlin at the end of April 1920, and the two immediately proclaimed unbounded admiration for each other as physicists and as human beings. Ehrenfest hoped that he and they would meet at the Third Solvay Conference in Brussels in early April 1921, but his hope was unfulfilled. Einstein, the only physicist from Germany who was invited to it in this bitter postwar atmosphere, decided instead to accompany Chaim Weizmann on a trip to the United States to help raise money for the new Hebrew University in Jerusalem. Bohr became so overworked with the planning and construction of his new Institute for Theoretical Physics in Copenhagen that he could only draft the first part of his Solvay report and ask Ehrenfest to present it, which Ehrenfest agreed to do following the presentation of his own report. After recovering his strength, Bohr invited Ehrenfest to give a lecture in Copenhagen that fall, and Ehrenfest, battling his deep-seated self-doubts, spent three weeks in Copenhagen in December 1921 accompanied by his daughter Tanya and her future husband, the two Ehrenfests staying with the Bohrs in their apartment in Bohr’s new Institute for Theoretical Physics. Immediately after leaving Copenhagen, Ehrenfest wrote to Einstein, telling him once again that Bohr was a prodigious physicist, and again expressing the hope that he soon would see both of them in Leiden.     

Energy loss straggling measurements for helium ions in Mylar and polypropylene polymeric foils

In the present contribution, we report results on energy straggling of He ions penetrating Mylar and polypropylene thin polymeric foils. The measurements were performed in the 900–3000 keV incident particle energy range by using the indirect transmission technique developed previously. The experimental straggling data are corrected to consider the roughness effects due to target thickness inhomogeneity. As expected, the roughness contribution to straggling is more important for helium than for proton ions and decreases as the ion energy increases. At low velocities, (<500 keV/amu), the variation of the experimental energy straggling results differs strongly from predictions based on Bohr’s formalism, and with increasing energies, the experimental results approach gradually the Bohr values.     

Meanvalue picture and ‘equivalent potential’ for a stochastic gluon background field

The main results (energy spectrum and the wave function at the origin) of a model with a stochastic gluon background field — the model of Dosch and Marquard — are alternatively achieved by the so-called meanvalue picture. In this approach it is not necessary to know the details of the stochastic process, therefore the formulas in this meanvalue picture emerge very simply. A local ‘equivalent potential’ to the stochastic process is deduced which reproduces with high accuracy the results of Dosch and Marquard for all values of the gluon correlation time. At last we compare this ‘equivalent potential’ with the well-known linear potential of Eichten et al.     

Entanglement Between Demand and Supply in Markets with Bandwagon Goods

Whenever customers’ choices (e.g. to buy or not a given good) depend on others choices (cases coined ‘positive externalities’ or ‘bandwagon effect’ in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one—in which case one says that the customers coordinate. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? In this paper we show that the interaction between demand and supply is even more complex than expected, leading to what we call the curse of coordination: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model and to a model introduced in social sciences by T.C. Schelling in the 70’s.     

On the possibility of measuring the electron spin in an inhomogeneous magnetic field

It is widely held that Bohr has shown that the spin of a free electron is not measurable. We point out that Bohr's argument has some important ifs and buts. A concrete configuration is calculated to produce a clear spin separation. This is then shown not to contradict Bohr's reasoning.     

A ‘Mixed’ Type Electron Interference Theory

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Spin-charge fluctuations in itinerant helical magnets

Using a generalized random phase approach quantum fluctuations beyond the helical mean-field states of the Hubbard model off half filling are discussed. The collective mode spectrum is shown to exhibit spin-charge mixing and is found to be strongly renormalized by coupling to low-energy incoherent particle-hole excitations. Results for the collective mode dispersion which displays a significant anisotropy are presented for selected helical phases. Moreover phase space regions of ‘missing’ modes are identified with a finite wave length instability of the helical states suggesting novel inhomogeneous phases of the doped Hubbard model. P.A.C.S. : 71.27.+a, 75.30.Fv, 75.40.Gb     

Advances in Carbon Nanomaterials: Science and Applications,by Nikos Tagmatarchis

It has recently been realized that there is more than one kind of superconductor, and we now recognize superconducting metals and alloys as being either ‘type-1’ or ‘type-2’. The ‘new’ type-2 superconductors can exist in a state which allows them to carry isrestanceless currents even in very strong magnetic fields, and they are used to construct very powerful electromagnets. This article describes the properties of type-2 superconductors, why very strong magnetic fields are required to drive them normal and why under certain circumstances they can carry large lossless currents.     

Applications of catastrophe theory to the physical sciences

Catastrophe Theory was introduced by René Thom in the late 1960's, as an attempt to model morphogentic changes in nature using ideas from topological dynamics and the theory of singularities of mappings. Thom envisaged a very general approach to topological changes in the solutions to parametrized systems of equations (such as differential and difference equations), and in particular discussed the special case of ‘elementary’ catastrophe theory: singularities of smooth real-valued functions. Popular expositions have tended to overemphasize this special case, but it remains the major source of ideas and methods.Here we survey the applications of Catastrophe Theory to the physical sciences (physics, chemistry, engineering, fluid mechanics, etc.). For brevity we confine attention to an area lying between ‘elementary’ and ‘general’ Catastrophe Theory, usually known as Singularity Theory. This is the theory of singularities of smooth vector-valued functions, which mathematically is a straightforward (though non-trivial) generalization of the real-valued case. In the last few years it has developed into a powerful and useful technique in several areas of theoretical physics, notably optics and bifurcation theory. Equivariant Catastrophe Theory, taking account of symmetry, is likely to prove especially interesting.     

The Franck-Hertz Experiments, 1911–1914 Experimentalists in Search of a Theory

In 1911, James Franck and Gustav Hertz began a collaboration to investigate the nature of collisions of slow electrons with gas molecules that led to a series of carefully planned and executed experiments, culminating in their discovery of inelastic collisions of electrons with mercury vapor atoms in 1914. This paper tells the story of their collaboration and the eventual reinterpretation of their results as a confirmation of Niels Bohr’s new atomic theory, largely as a result of experiments done in North America during the Great War.     

Quantum Entanglement in Concept Combinations

Research in the application of quantum structures to cognitive science confirms that these structures quite systematically appear in the dynamics of concepts and their combinations and quantum-based models faithfully represent experimental data of situations where classical approaches are problematical. In this paper, we analyze the data we collected in an experiment on a specific conceptual combination, showing that Bell’s inequalities are violated in the experiment. We present a new refined entanglement scheme to model these data within standard quantum theory rules, where ‘entangled measurements and entangled evolutions’ occur, in addition to the expected ‘entangled states’, and present a full quantum representation in complex Hilbert space of the data. This stronger form of entanglement in measurements and evolutions might have relevant applications in the foundations of quantum theory, as well as in the interpretation of nonlocality tests. It could indeed explain some non-negligible ‘anomalies’ identified in EPR-Bell experiments.