The scattering problem in quantum mechanics as an eigenvalue problem

A method is proposed which allows the scattering problem to reduce to the eigenvalue problem. Unlike the usual method when the scattering phase is extracted from the asymptotics of solution of the Cauchy problem at a given collision energy, in the proposed method the collision energy is obtained from the solution of the Sturm-Liouville problem at a given scattering phase. The continuous analog of the Newton method is used for the numerical realization of the proposed method.     

Gravitational effects in quantum mechanics

To date, both quantum theory and Einstein’s theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be unified, and by now, there exists strong theoretical arguments pointing to the necessity of quantising the gravitational field. In recent years, a number of experiments have been proposed which, if successful, should give insight into features at the Planck scale. Here, we review some of the motivations, from the perspective of semi-classical arguments, to expect new physical effects at the overlap of quantum theory and general relativity. We conclude with a short introduction to some of the proposals being made to facilitate empirical verification.     

Landau problem in noncommutative quantum mechanics

The Landau problem in non-commutative quantum mechanics (NCQM) is studied.First by solving the Schr(o)dinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity.Then we discuss the noncommutative phase space case,namely,space-space and momentum-momentum non-commutative case,and we get the explicit expression of the Hamfltonian as well as the corresponding eigenfunctions and eigenvalues.     

Landau problem in noncommutative quantum mechanics

The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrodinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues.     

The problem of objectification in quantum mechanics

The hypotheses of weak and strong objectification of quantum mechanical observables, as well as theoretical arguments and experimental evidence against these hypotheses, are systematically reviewed.     

Remote two-time boundary conditions and special states in quantum mechanics

For an oscillating universe, the assumptions of wave-function localization and approximate symmetry for the initial and final states impose restrictions on the intermediate motion. We argue that one of these restrictions is the avoidance of superpositions of macroscopically distinct states.     

The problem of decay in nonrelativistic quantum mechanics

In this paper the time-dependent Schrödinger equation with an arbitrary potential with finite effective radius is solved. Outside the effective radius of the potential a universal solution is obtained which does not depend on the initial state and which describes the evolution of a resonance state. In the single-resonance approximation various space-time domains are studied in which an exponential decay law can be observed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 38–43, December, 1972.     

Wave packet reduction in quantum mechanics: A model of a measuring apparatus

We investigate the problem of wave packet reduction in quantum mechanics by solving the Schrödinger equation for a system composed of a model measuring apparatusM interacting with a microscopic objects. The instrument is intended to be somewhat more realistic than others previously proposed, but at the same time still simple enough to lead to an explicit solution for the time-dependent density matrix. It turns out that,practically, everything happens as if the wave packet reduction had occurred. This is a consequence of the fact that the apparatus is made up of a very large number of microsystems interacting withs. More precisely, our model shows that the macroscopic size of a measuring apparatus can lead by itself to a density matrix for the systemM + s which is physically equivalent to the density matrix of a statistical mixture corresponding to the reduced wave packet.     

量子数n和l对束缚电子径向波函数的影响

利用Hartree-Fork平均自洽场理论,研究了主量子数n和角量子数l对束缚电子波函数影响的主要特征.原子实通常是致密、紧凑的,当n和l较大时价电子的行为将与相应的氢原子电子相似;在靠近核的原子实区域,原子实的影响使价电子径向波函数节点的位置几乎重合.在近核区域离心势可对电子产生很大影响:小l电子只能轻微地贯穿到原子实的较深区域,对大l电子离心势将阻止其深入到离核很近的原子实内;离化度较高时离心势的作用相对减弱,电子深入到原子实内的可能性较大.     

Consistent histories and the interpretation of quantum mechanics

The usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times, called consistent histories, through a criterion which ensures that, within limits which are explicitly defined within the formalism, classical rules for probabilities are satisfied. The interpretive scheme which results is applicable to closed (isolated) quantum systems, is explicitly independent of the sense of time (i.e., past and future can be interchanged), has no need for wave function collapse, makes no reference to processes of measurement (though it can be used to analyze such processes), and can be applied to sequences of microscopic or macroscopic events, or both, as long as the mathematical condition of consistency is satisfied. When applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics, though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus.     

玻恩对量子力学的实际贡献初探

玻恩和海森伯在矩阵力学创建过程中的各自贡献,在许多相关物理学史著述中已有"定论",即基本上都认为海森伯是矩阵力学的创立者,而玻恩只是伯乐,仅在数学方面对矩阵力学的建立有一定具体贡献.然而据我们所得到的大量文献却无可辩驳地说明,事实并非如此.经过多年探索,玻恩的哥廷根学派做好了建立量子力学的从数学到思想的所有必要的前期准备工作,海森伯取得的突破只是这些准备下的必然的延拓.本文除必要的分析外,尽量更多依靠引用足够的权威文献来得出可靠结论,相信这样更有说服力,更易于改变人们的成见.     

半导体量子阱中激子波函数及其 Fourier系数的计算和应用

利用准玻色子方法发展的激子动力学方程是研究半导体纳米结构中激子超快动力学的有效理论手段. 为了将这种方法应用于半导体量子阱, 需要知道量子阱中的激子波函数及其在动量空间的表示, 从而得到激子动力学方程中所必须的系数. 详细讨论了理想和实际量子阱中的激子波函数, 特别是其在动量空间的表示, 并进一步讨论了激子动力学方程中所必须系数的计算方法. 通过求解这些系数, 对量子阱中因激子密度变化而引起的太赫兹脉冲作用下激子能级间跃迁过程中的非线性效应进行了理论预测, 得到了与实验符合很好的结果.     

用X射线衍射仪测量康普顿散射的波长改变

详细阐述了利用多晶X射线衍射仪测量康普顿散射射线波长的实验方法和实验结果.     

Gasket temperature: an alternate technique for estimating sample temperature in a multi-anvil apparatus

It is common for sample temperatures to be estimated by the power input to the furnace in multi-anvil experiments in which a thermocouple cannot be used or the thermocouple failed during heating. Uncertainties using this technique are often on the order of ±85°C or larger. This paper describes a new method for estimating sample temperature using a second thermocouple outside all pressure media. Temperatures recorded at this external (gasket) thermocouple trend linearly with the internal (sample) thermocouple temperature. Because of thermal lag, it is necessary to determine the first gasket temperature (T₀) corresponding to the desired sample temperature. Accurate prediction of T₀ for the desired sample temperature can come from relatively few (5–6) gasket-temperature measurements made during the initial temperature ramp over a small temperature range (500–600°C). Using this method and manually ramping to T₀ allows for uncertainties in sample temperature estimation as small as ±20°C.     

Functional analysis and quantum mechanics: an introduction for physicists

We give an introduction to certain topics from functional analysis which are relevant for physics in general and in particular for quantum mechanics. Starting from some examples, we discuss the theory of Hilbert spaces, spectral theory of unbounded operators, distributions and their applications and present some facts from operator algebras. We do not give proofs, but present examples and analogies from physics which should be useful to get a feeling for the topics considered.     

The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem

A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement.     

A study of transverse charge density of pions in relativistic quantum mechanics

The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.