With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position (a) and momentum (p) increases with decreasing radii. The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen atom only. A relation between uncertainties and pa is for future study.
With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position (a) and momentum (p) increases with decreasing radii. The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen atom only. A relation between uncertainties and pa is for future study.
Background: There has been altercation for and against Heisenberg uncertainty principles, whose earlier mathematical form has assumed other forms. This is despite the fact that the original form ought to be for the hydrogen atom only. Methods: the method is purely theoretical and computational, involving the use of spectroscopic data in the literature. Aim and objectives: The aim of the research was to show that half of reduced Planck’s constant (ℏ/2) cannot be restricted to a lower limit to the product of the uncertainty in the momentum and the uncertainty in the position. The objectives were: 1) to undertake the derivation of an equation unifying the Heisenberg uncertainty principle and atomic principles; and 2) to give evidence that half of the reduced Planck’s constant (ℏ/2) is strictly for hydrogen. Results and discussion: With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position and momentum increases with decreasing radii. Conclusion: The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen only. The possibility of linking the product of uncertainties in position and momentum to Pa may be reserved for a future study.
This research examines the probability percentage of the existence of the hydrogen atom's electron in the space surrounding the nucleus of the mentioned atom. From the calculations of the semi-classical Bohr atomic model, a specific radius for the hydrogen atom's electron was obtained (with good approximation a_0=5.3×〖10〗^(-10) m); However, after the wave property of particles was introduced and this property was extended to the electron, Schrödinger formulated the wave equation of matter and its probabilistic physical interpretation was proposed by Born. In this paper, by applying the Schrödinger equation to the hydrogen atom, we aim to determine the probability of finding the electron of the hydrogen atom at the Bohr radius, as well as at distances smaller and greater than it.
Abstract The Heisenberg uncertainty relations are cornerstones of quantum theory. Yet care is required in applying them. While they determine the lowest energy level in some systems, such as the isotropic three-dimensional harmonic oscillator, they fail to do so in other systems, notably, the hydrogen atom. This failure has been overlooked in many textbooks and pedagogic articles. The failure arises due to the singularity of the Coulomb potential. To elucidate the point, we present four subfamilies of position probability distributions. By delineating the limitations in applying position-momentum uncertainty to the hydrogen atom, we hope to improve the teaching and learning of modern physics.
Concern has been expressed against the new theories, Heisenberg uncertainty principle (HUP) and Schrödinger wave/quantum mechanics (SE) that are purported to have replaced Bohr’s theory and equation. The research was undertaken with the following objectives: 1) to review concerns about atomism; 2) appraise the issues of mathematical complexities in HUP and SE; 3) review criticism against SE and HUP; 4) most importantly derive a Planck constant invariant equation for the calculation of any atomic radii; and 5) re-calculate the radii of selected elements chosen for their biological importance. The theoretical research with calculations, showed that the opposing theories are criticised because, they are obsessed with mathematical complexities with ambiguities without common ground that should usher alternative solution to the problem of the size of atom and thus, they cannot be considered as a valid description of reality. Bohr’s equation and variants of it and the Planck constant invariant equation (Eq. (15)) derived in this research are regarded as deterministic in nature and were capable of reproducing Bohr’s radii for any atom; the radii were also capable of reproducing the average ionisation energies of hydrogen and oxygen atoms, chosen for illustration only, when substituted into derived preliminary equation (Eq. (10)).
The purpose of this study is to analyze the probability and uncertainty of electron linear momentum in with the Heisenberg uncertainty approach. Measurement of the position and momentum of atomic electrons is probabilistic. The probability and uncertainty of electron linear momentum are analysed analytically, and simulations of hydrogenic atoms' normalized radial wave function are performed. they can be viewed as hydrogenic atoms with only one electron orbital. The probability and uncertainty of electron linear momentum in decrease with increasing values of the principal quantum number n ≤ 3. While the uncertainty of the electron position is increasing. The results of this study are in accordance with the characteristics of position and linear momentum that are not commutable. The increase in the value of the main quantum number means that the electron's position against this is getting farther, and the speed in the orbital is getting smaller.
Most of the physicians that I know are chary of Physics, especially the theory of elementary particles. Even if in Isaac Newton's mathematically precise universe, everything follows clear-cut laws and predictions are easy given appropriate starting conditions. Perhaps, however, physicians coping with this uncertainty will perhaps feel more in tune with Heisenberg's uncertainty law. Heisenberg (1901–76) described a theory of quantum mechanics, published in 1925, when he was only 23 years old. The uncertainty principle describes an imprecision in nature resulting in a limit to what we can know about the behaviour of quantum particles and, hence the smallest scales of nature. Heisenberg was awarded the Nobel Prize for Physics for 1932 for this theory and its application that resulted amongst other things the discovery of allotropic forms of hydrogen. His theory stated that we cannot always give an electron a position in space at a given time, nor follow it in its orbit, so that we cannot assume that the planetary orbits proposed by Niels Bohr exist. Mechanical quantities, such as position and velocity, should be represented, not by ordinary numbers, but by abstract mathematical structures called ‘matrices’ and he formulated his new theory in terms of matrix equations. The principle of uncertainty, says that the determination of the position and momentum of a mobile particle necessarily contains errors the product of which cannot be less than the quantum constant h and that, although these errors are negligible on the human scale, they cannot be ignored in studies. We cannot measure the position (x) and the momentum (p) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. There are many ways of looking at this and in medicine we need to take account of uncertainty. Uncertainty in medicine can be resolved in many ways and can include Occam's razor. In medicine, all presenting symptoms in a patient may be explained by a few possible causes. In medicine, all presenting symptoms in a patient may be due to several disease and social processes at the same time. How can this be relevant to a working physician? The whole of medical practice has parallels with the certainties of Newton and Bohr. The object of a clinical consultation is to give a sign or complaint a diagnostic named description to be followed by a treatment regime which resolves the problem. Yet every physician knows and automatically models his understanding of a clinical problem perhaps unknowingly on a model based on Heisenberg's uncertainty principle. A core process, which is complicated by factors understood or not. The same principles are relevant to so many other features of life. There are certain fixed points in the diagnostic and clinical process. Gender, race, age, weight to height ratio, privileged and social life and intelligence. Some people age at different rates to their age cohort? Similarly, obesity does not always matter. The patient′s family history is another variable, complicated occasionally when the putative father with a family health trait may not be the actual father. The social story is a minefield, with the possibility of every phase of a person’s life being of relevance. A further element is how well the physician and the patient and their caring team relate. The clinical examination then gives a further array of data. From all of this comes a diagnosis which gives a pathway to a treatment schedule the ability of the patient to manage their treatment regime becomes important. There is a tendency that as soon as the diagnosis is made then the other elements fade away from the care plan, though of course it persists in the person's life. We are all consciously or unconsciously aware of the complex fabric of clinical care. It is intriguing to appreciate that other disciplines have been presented with the same multifactorial uncertainties. The era in Physics when Heisenberg introduced his view of nuclear physics was one when a precise physical model was being completed and gave certainty to a complex problem. His principle while obviously reintroducing uncertainty gave freedom of thinking and allowed further fruitful progress. We physicians do not enjoy uncertainty, and to have it formalized is uncomfortable. So we instinctively identify the major problem and treat that. By and large this is a useful process. It is however important to see this as a convenience. A convenience that may not always suit the patient. Applying the Heisenberg principles gives a broader view of a patient's concerns and problems and better care.