Bohr's Quantum Research Articles

How Einstein prevents Bohr's quantum mechanics from being a fundamental theory

This paper uses a limited scope to present an explanation of how quantum jumps prevent quantum mechanics from being a fundamental theory, and this paper explains how Einstein's theory that radiation conveys inertia between the emitting and absorbing bodies plays a critical role in the presented explanation.

Ceteris Paribus Laws and the Concept of Capacity in the Philosophy of Science of Nancy Cartwright

A brief introduction to Nancy Cartwright’s philosophy of science is presented along with an analysis of several of her thoughtful and controversial views. Nancy Cartwright came to revolutionize the philosophy of science by presenting original and provocative philosophical positions using specific concepts such as: capacity, ceteris paribus laws, nomological machines, among others. In this article it is shown that some of nature fundamental conservation laws, such as energy, momentum and angular momentum, cannot be ceteris paribus. Also, it is discussed among other quantum mechanical examples, the application of the concept of capacity to Coulomb interactions and Bohr quantum mechanics postulates for the hydrogen atom.

On the Principle of Least Action

Investigations into the nature of the principle of least action have shown that there is an intrinsic relationship between geometrical and topological methods and the variational principle in classical mechanics. In this work, we follow and extend this kind of mathematical analysis into the domain of quantum mechanics. First, we show that the identification of the momentum of a quantum particle with the de Broglie wavelength in 2-dimensional space would lead to an interesting feature; namely the action principle S=0 would be satisfied not only by the stationary path, corresponding to the classical motion, but also by any path. Thereupon the Bohr quantum condition possesses a topological character in the sense that the principal quantum number is identified with the winding number, which is used to represent the fundamental group of paths. We extend our discussions into 3-dimensional space and show that the charge of a particle also possesses a topological character and is quantised and classified by the homotopy group of closed surfaces. We then discuss the possibility to extend our discussions into spaces with higher dimensions and show that there exist physical quantities that can be quantised by the higher homotopy groups. Finally we note that if Einstein’s field equations of general relativity are derived from Hilbert’s action through the principle of least action then for the case of n=2 the field equations are satisfied by any metric if the energy-momentum tensor is identified with the metric tensor, similar to the case when the momentum of a particle is identified with the curvature of the particle’s path.

The historical role of the Adiabatic Principle in Bohr's quantum theory

It is widely known that both the Correspondence Principle and the Adiabatic Principle were the two pillars of Bohr's quantum theory. However, the Correspondence Principle usually gets much more attention in historical accounts. A closer look at Bohr's quantum theory shows that, although the fate of the Adiabatic Principle was closely tied up with the validity of mechanics, it also played a significant role in the old quantum theory. In the early 1920s, when dealing with multielectron atoms, Bohr was forced to reshape the theory and thus to reconsider the relative relevance of the two principles. It is precisely the late preponderance of the Correspondence Principle which has, in perspective, biased the historical weight attributed to each of them.

Centenary of the Franck‐Hertz experiments

In 1925 the Nobel Prize in Physicswas awarded jointly to James Franck(1882–1964) and Gustav L. Hertz(1887–1975) “for their discovery ofthe laws governing the impact of anelectron upon an atom” [1]. Theyconducted an ingenious set of exper-iments in 1913 and 1914 in whichthey measured the ionization po-tential of different gases [2]; stud-ied collisions between gas moleculesand slow electrons [3]; developed atheory of ionization by collision [4];determined the ionization potentialof mercury vapor with the methodof electron collision [5]; and car-ried out spectroscopic experimentswith mercury vapor which yieldedthe spectral line 253.6

Computer Simulations of Quantum Theory of Hydrogen Atom for Natural Science Education Students in a Virtual Lab

The present article is primarily targeted for the advanced college/university undergraduate students of chemistry/physics education, computational physics/chemistry, and computer science. The most recent software system such as MS Visual Studio .NET version 2010 is employed to perform computer simulations for modeling Bohr's quantum theory of hydrogen (H) atom in class-setting of a virtual laboratory. The necessary computer algorithm is developed to compute discrete values of the orbit radius, and stationary energy levels of Bohr's H-atom. More than 2000 computer simulations are performed to investigate the quantum model behavior starting from the ground state of H-atom until we reached the energy continuum. One of the natural consequences of Bohr's model is that it could provide a perfect corroboration of the experimentally observed spectrum of H-atom with that empirically obtained from formulas derived by famous scientists of 19th and 20th centuries. Using old theory of classical electrodynamics, it was not possible to explain the observed line spectrum of H-atom. Bohr's quantum model of H-atom set the stage for the development of a modern branch of physics and chemistry in microscopic world, the so called quantum mechanics and very recently of a new computing technique known as quantum computing.

Refocusing Bohr's quantum postulate

As recently noted by Landsman, the postulate claimed by Bohr to characterize the essence of quantum theory has not played a major role in modern formulations of the theory. Folse has argued that the postulate nonetheless served a key role in Bohr's development of the “wholeness” and complementarity that underlie standard quantum-mechanical calculations. This paper presents one way to bring the main ideas of the quantum postulate into a sharper focus, one that addresses more directly how quantum mechanics is applied in the analysis of experimental results, and also leads to a useful criterion in evaluating counterfactual assertions about certain kinds of atomic-level measurements.

Fundamental theories and their empirical patches

Many theories require empirical patches or ad hoc assumptions to work properly in application to chemistry. Some examples include the Bohr quantum theory of atomic spectra, the Pauli exclusion principle, the Marcus theory of the rate-equilibrium correlation, Kekule’s hypothesis of bond oscillation in benzene, and the quantum calculation of reaction pathways. Often the proposed refinements do not grow out of the original theory but are devised and added ad hoc. This brings into question the goal of constructing theories derived from first principles and the concept of ranking the merit of theories according to their freedom from empirical contamination.

Quantum optics with interacting polaritons

AbstractRecent theoretical and experimental investigations evidencing quantum optical effects in semiconductor microcavities are reported. In particular the results of an experiment that probes polariton quantum correlations by exploiting quantum complementarity are described. In this experiment, it has been shown that polaritons in two distinct idler modes interfere if and only if they share the same signal mode so that which‐way information cannot be gathered, according to Bohr's quantum complementarity principle. The experimental results prove the existence of polariton pair correlations that store the which‐way information. This interpretation is confirmed by a theoretical analysis of the measured interference visibility in terms of quantum Langevin equations. The devised experimental scheme employs two frequency‐degenerate mutually‐coherent pump modes. It is shown that this kind of two‐pump parametric schemes can be exploited to realize a number of interesting tasks as the emission of polarization‐entangled cavity‐polariton states and the coherent control and trapping of parametric amplification in SMCs. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

From Propagation to Structure: The Experimental Technique of Bombardment as a Contributing Factor to the Emerging Quantum Physics

I observe that quantum physics emerged at the turn of the last century when physics had shifted its concern from propagation phenomena to questions of structure. This transition materialized with the development of a new experimental technique, the bombardment method. The transition is well exemplified by the move from the experimental studies of Heinrich Hertz to those of Ernest Rutherford, and from those of Heinrich Hertz and Philipp Lenard to those of James Franck and Gustav Hertz. I trace the history of Rutherford's experimental bombardment method as it emerged from nineteenth-century propagation studies. I then demonstrate the use of the bombardment method in another experimental context, namely, in the celebrated experiment of Franck and Hertz. I locate the root of this experiment in Lenard's experimental studies and analyze Franck and Hertz's flawed interpretation of it. I conclude by underlining the crucial role that Bohr's quantum theory of the atom played in helping to establish these bombardment experiments as milestones of modern physics.

Universal behaviour of the electronic transport

The universal behavior of the electronic transport in solids is discussed. It is shown that these findings can be interpreted by a general quantum transport model. It is based on a generalization of the Bohr quantum condition, resulting in a reference length ae = 7.25 nm and a reference electron density of 3 × 1015 m-2, which limits the electron current. It is shown that the limitation is supported by experimental data. The priority of the formulation of the square of the electric charge as e2 = αh is discussed. It leads to a new system of units. The formulations of the reference values of all electromagnetic quantities are given. It is shown that the data of the Aharonov Bohm effect of 1/f noise confirm the presented statements.

Quantum jumps in atomic systems

The authors summarise the principal aspects of the recent discussion regarding the observation of Bohr's quantum jumps in resonance fluorescence from three-level systems. The experimental results are reviewed and possible applications are given.

Elementary quantum physical description of triplet superconductors

The elementary quantum physical description of superconductors using only three elementary facts of quantum physics, Bohr's quantum principle, the uncertainty relation and Pauli's exclusion principle, can reflect the basic bulk properties of superconductors, the effect of temperature and external magnetic fields. The same method for triplet superconductors, gives that for every H ≠ O magnetic field the perfect conductor state is thermodynamically more favourable, than the diamagnetic state; the perfect conductor state will cease at H=Hc2.

Acoustic tomography by Hamiltonian methods including the adiabatic approximation

Long‐range acoustic propagation for ocean tomography is elegantly described by invoking a Hamiltonian formulation. Many results previously derived in an ad hoc manner emerge naturally from the use of the Hamiltonian. The cycling between the upper and lower ocean that is characteristic of oceanic sound propagation is treatable as a libration phenomenon. General perturbation methods, highly developed in astronomy and quantum mechanics, are immediately available for understanding both range independent and range dependent disturbances to a reference profile. The tomographic two‐point boundary value problem leads, in an analogy to the old Bohr quantum mechanics, to quantization of the action, although the more naturally quantized variable is the canonical angle. An adiabatic approximation merges naturally from the formalism. In the adiabatic approximation the range dependent bias problem in tomography can be fully understood and accounted for as long as the source and the receiver remain axial.

Observation of quantum jumps.

We have recorded the laser-excited resonance fluorescence of one to three ${\mathrm{Ba}}^{+}$ ions and observed Bohr's quantum when an ion decayed to the metastable $^{2}D_{\frac{5}{2}}$ state, suddenly quenching its fluorescence. Most of the jumps mark Raman-Stokes scattering from the $^{2}S_{\frac{1}{2}}$ and $^{2}D_{\frac{3}{2}}$ levels.

Stationary Kepler orbits of the electron with velocity-dependent perturbations — classical quantization

In this paper the evolution of Kepler orbits generated by velocity-dependent perturbations is discussed. It is found that in the presence of oscillatory perturbations, of oscillation frequency proportional to the kinetic energy of the moving particle, a discrete set of stationary orbits exists. If the coefficient of proportionality in the frequency—kinetic energy relation is the Planck constant, the orbits are the same as those given by Bohr's quantum postulates. The conclusion is drawn that the Schrödinger wave equation describes, in hidden form, velocity-dependent oscillatory perturbations superimposed upon the basic motion of an electron and has nothing in common with the basic trajectory of the motion.

ELEMENTS AND THEIR ISOTOPES

THE Ritchie Lecture for 1945 of the Royal Society of Edinburgh was delivered by Dr. N. Feather (then at the Cavendish Laboratory, Cambridge, and now professor of physics at the University of Edinburgh), who took as his subject “The Number of the Elements”. The lecture has now been published (Proc. Roy. 8oc. Edin., A, 62, Pt. 2, 211 ; 1946). Prof. Feather commenced by tracing the development of the idea of the chemical element from its earliest beginnings until, in the last quarter of the nineteenth century, Mendeléeff's Periodic Table became accepted as fundamental. Further elucidation of the Periodic Table had to wait for the emergence of the nuclear model of the atom as described by Rutherford in 1911. This led to the Bohr quantum theory, Moseley's work, Soddy's idea of isotopy and Aston's mass analysis. Physicists found that the nucleus could be adequately specified by two parameters, Z and A : the former, the atomic number, is a measure of the positive nuclear charge, and the latter, the mass number, the nearest integer to the number expressing the mass of the corresponding neutral atom in terms of chemical oxygen as 16. The elements were defined and distinguished by their Z-values. By 1932 nearly all the different atom types had been identified and classified according to their Z- and A-values. In 1932, Chadwick discovered the neutron (Z = 0, A = 1), and the nuclear picture was much simplified by regarding the nucleus as made up of heavy particles, neutrons and protons (Z = 1, A = 1). The mass defect, or 1/c2 times the energy of binding of the nucleus, can be estimated as the difference in mass between that of the actual nucleus and of its constituent protons .and neutrons taken separately. It is important to note that the mass defect increases approximately linearly with A ; and that this, together with other known facts, leads to the conclusion that intra-nuclear forces show saturation with the ?-particle as the quasi-saturated unit.

A Note on Local Momentum in Wave Mechanics

The present paper shows the exact relations between dynamical quantities of classical theory and their wave mechanical analogues. A new quantity local momentum is defined and discussed and the Bohr quantum condition is revived in a form compatible with modern theory.

The Place of X-ray Crystallography in the Development of Modern Science

VON LAUE'S discovery of the diffraction of X-rays by crystals effectively provided science with a new eye with which to see the ultimate arrangement of the nuclei and electrons of solid matter. It is true that X-ray analysis does not show atoms and electrons to the eye in the way that a microscope does; the process of interpretation is more complicated, but it is essentially analogous. In an ordinary optical instrument the interference of rays from luminous points is used to build up the optical image by means of a lens system. In X-ray analysis the interference pattern is taken and interpreted mathematically instead of optically to give the nature of the object observed, so that it is just one step farther removed from our inherited mechanism for appreciating the external world. Now we have had this new eye only seventeen years, and although it has shown many marvellous things and enabled us to build for the first time a picture of the intimate structure of solid matter, we cannot believe that it has more than begun to be used. Many more important discoveries are bound to follow from it, and it has still to find its place as an essential instrument in every branch of scientific research. The object of this article is to point out what can already be seen of its possibilities and how it is likely to affect science in the near future. The Three Forms of Information from X-ray Diffraction Apart from the knowledge given on the nature of X-rays—which was of such critical importance in the discovery of atomic numbers and in the verification of Bohr's quantum theory of radiation—the diffraction of X-rays by crystals yields information about three grades of fine structure of matter. Ultimately the diffraction of X-rays is due to the interaction of the radiation with the electrons in the atoms of matter, and so the deepest information it can give is on the position of the electrons in the individual atoms, or, more correctly, information as to the average distribution of density of negative electricity. Here it is most closely related to pure physics and leads to the possibility of the complete description of the state of any piece of matter. But without going nearly so deeply, X-rays can show the position of the maxima of electrical density, that is, the position of each kind of atom, in a regular crystalline structure. It is in this field that the chief work of X-ray crystallography has been done. It is faced with the extensive problem of determining all the different possible types of atomic arrangement in solid substances, which has such a clear bearing on chemistry.

The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohr's Quantum Theory

The Dielectric Constant of Atomic Hydrogen from the Point of View of Bohr's Quantum Theory