The process of observation disturbs the thing being observed and that disturbance might possibly affect other observations. Heisenberg showed that simultaneous measurements of an electron's position and its momentum interfere with each other and thus induce essential uncertainties into those measurements. Quantum mechanics represents the behavior of electrons around nuclei in terms of mathematical constructs called wave functions, or orbitals, which contain all possible information about the electron. The square of the wave function gives the probability of finding the electron in a given region of space. For mathematical reasons, physicists and chemists almost always use the abstract concept of wavefunctions (orbitals), rather than that of electron probability clouds, to describe electrons. The distribution of probability within a probability cloud is not uniform. For some, the greatest probability is near, or even at, the nucleus
The process of observation disturbs the thing being observed and that disturbance might possibly affect other observations. Heisenberg showed that simultaneous measurements of an electron's position and its momentum interfere with each other and thus induce essential uncertainties into those measurements. Quantum mechanics represents the behavior of electrons around nuclei in terms of mathematical constructs called wave functions, or orbitals, which contain all possible information about the electron. The square of the wave function gives the probability of finding the electron in a given region of space. For mathematical reasons, physicists and chemists almost always use the abstract concept of wavefunctions (orbitals), rather than that of electron probability clouds, to describe electrons. The distribution of probability within a probability cloud is not uniform. For some, the greatest probability is near, or even at, the nucleus
Einstein’s 1905 paper on the photoelectric effect, in which he considered Planck’s idea of quanta of energy to be a universal characteristic of light, marks the beginning of quantum theory. Electrons and other quantum particles behave like particles and like waves, depending on the particular observation. An electron occupies a position in space only when an observation is made. Heisenberg decided that the problem of the actual orbits of the electrons inside the atom should be ignored; they have no meaning. Schrodinger reasoned that if an electron has a wave-like behavior, then it should be possible to describe this behavior in space and time by a wave equation. Soon after it was discovered that high-speed electrons had wavelengths that were much shorter than the wavelengths of light, physicists showed that magnetic fields could act as lenses by causing electron waves to converge to a focus.
Quantum mechanics has been enormously successful in explaining the behavior of microsystems such as molecules, atoms, and nuclei. We have seen that quantum mechanics describes a quantum system by the wave function ψ, which is the solution of the Schro¨dinger equation. The wave function determines the probability amplitudes (whose modulus squared gives the probability) for all possible outcomes of a measurement corresponding to an observable on the system. In general, the wave function does not uniquely predict the result of a measurement; it only provides a probability distribution for all possible results of the measurement on a quantum system. Only if the system happens to be in an eigenstate corresponding to the observable being measured, is the result of a measurement of this observable completely predictable. On the other hand, the results of measurements corresponding to a conjugate or non-commuting observable, on the same system in the same state, are indeterminate. Quantum mechanical description of physical systems raises profound questions: How are the wave function and the probabilities for different outcomes of a measurement to be interpreted? Does the wave function represent a single system or an ensemble of systems? Does the physical system actually have the attribute corresponding to the measurement in question or does the measurement itself create the attribute? These questions led to different interpretations of quantum mechanics, which were vigorously debated during the years of its discovery as also in the following decades. The new idea of indeterminacy was especially difficult to reconcile with the long-held view that a physical theory should aim at predicting accurately, and without ambiguity, the result of any measurement on any system, big or small. These debates not only gave us a deeper understanding of quantum mechanics but also changed profoundly the way we view the micro-world.
Wave equations -wave functions -are the mathematical way of describing the behavior of things in quantum mechanics. The physical basis of this is that on the microscopic level every object is at the same time both a particle a bundle of waves. So the mathematics that describes dynamics on this level turns out to be the mathematics of wave functions. Wave functions are far from being the easiest things in mathematics to solve compute with. To calculate the behavior of an atomic nucleus, for instance, involves working with dozens or hundreds of wave functions (each proton neutron has its own) that are related to one another in such a way that the solution to each one depends on all the others. They cannot be solved one by one; they have to be solved ensemble, dozens or hundreds of simultaneous equations, as mathematicians would describe By hand the task is formidable, perhaps practically impossible. However, at the Lawrence Livermore National Laboratory, a Cray 1, one of the latest, biggest fastest of computers has now come to the rescue. Using it M. S. Weiss co-workers have been able to calculate what happens in various kinds of collisions of a krypton nucleus with a lanthanum nucleus. Then, with the latest computer graphics they are able to display these processes in an animated film. The two nuclei approach each other, collide, in some cases fuse, in others come apart, everything is decorated with bright false colors representing the density levels of matter inside the nuclei. The pictures the information in them represent the solution of 146 simultaneous wave functions, one for every two nucleons, every two particles in the two nuclei. There is one function for every two nucleons rather than every one because the mathematics contains one important approximation. Nucleons can come with two directions of spin, spin up or spin down. This theory does not distinguish between the two spin states, so each function actually represents the average of one of each. The pictures show a dozen instances, starting from a head-on collision proceeding to instances of greater greater offset between the centers of the two nuclei until they arrive at a sideswipe in which the nuclei hardly touch each other. The collisions near head-on result in fusion. A little offset contributes an angular momentum: The fusion product rotates. More offset the nuclei collide, losing a lot of energy, but retaining enough to come apart again. This is known as deep inelastic scattering. Finally, an instance where the two nuclei do not touch, but where distortions vibrations are produced in them by the force between them when they are close. Weiss says the film wakes physicists up when he shows it at the end of a talk. He mentions one experimentalist who came up said how nice it was to be able to actually see these things. At least four levels of abstraction, Weiss comments, and he talks about seeing it. Yet viewing the film, one can understand what the experimentalist meant. The calculations behind the film are quite accurate in predicting the main events of the collisions, that is what is really important. According to Weiss, they predict accurately the conditions under which fusion is likely, the proper range of deep inelastic scattering so forth. In the pictures the behavior looks like that of a fluid, liquid drops coming together. Weiss stresses that it is actually the sum of discrete motions, those 146 individual wave functions. One of the purposes of the exercise was to see whether it was possible to derive a macroscopic theory that is, one that would give a simpler mathematical expression for the over-all behavior of the nuclei, that would yield the desired predictions without having to start from the 146 individual wave functions. It turns out, Weiss says, that a macroscopic theory is possible in some particular cases, but the microscopic one, starting from the individual wave functions, remains the general one. Computation was the serious hindrance to doing it before now. As Weiss says, the theory itself was written down years ago by P. A. M. Dirac, one of the pioneer theorists of quantum mechanics. It took Weiss co-workers a year to figure out how to feed the computation to the Each of the dozen collisions which takes about 10-21 seconds in real time, but is displayed in extreme slow motion in the film-took an hour of computation time using the core of the Cray That's expensive computing, but, says Weiss, I would never try it on a lesser computer. O
Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels. However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.
With an aim at the abstract conception of wave functions for hydrogen atom in quantum mechanics,this paper suggests the radial distribution,angular distribution and spatial distribution function of hydrogen atom electronic cloud,and also,Matlab software is used to plot their corresponding distribution charts.The analytical results indicate that the distribution patterns of hydrogen atom electronic clouds are co-determined by the radial and angular probability distribution,and that the electronic cloud distribution density is so uneven that the orbit trace can be observed.Accordingly,this method can reveal the radial,angular and spatial probability distribution laws of hydrogen atom electronic clouds intuitionally,whereby a new thinking way for analyzing the abstract wave function visualization in quantum mechanics is provided in this paper.
Electron spin and orbital interaction outside the nucleus is a classical and important problem in quantum mechanics. In this paper, a simplified model is constructed for the phenomenon of atomic energy level splitting in weak magnetic field in quantum mechanics, and the wave function of the fine structure of hydrogen-like atoms under perturbation is derived. According to the probability interpretation of quantum mechanics, we obtain the probability density function of the fine structure electron cloud of hydrogen-like atoms. The Monte Carlo selection method is used to sample, and the electron cloud images under different quantum numbers are drawn by Mathematica software. The experimental results are explained regularly, so that people can intuitively understand the distribution of electron cloud in three-dimensional space.