While in the process of studying hydrogen atom wave function in quantum mechanics course,some frequently-asked questions about the radial probability distribution,tree-dimensional angular distribution,and movement trace are raised by beginners.The visualized interpretations for those questions are made by the three dimension model set up in computer,which can not only help students to establish the correct quantum images about the movement of the particles,but also provide a reference for visualization about other quantum phenomena.
While in the process of studying hydrogen atom wave function in quantum mechanics course,some frequently-asked questions about the radial probability distribution,tree-dimensional angular distribution,and movement trace are raised by beginners.The visualized interpretations for those questions are made by the three dimension model set up in computer,which can not only help students to establish the correct quantum images about the movement of the particles,but also provide a reference for visualization about other quantum phenomena.
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called “common sense” based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
In the previous chapter we saw that for a particle in a one-dimensional potential well, physically acceptable solutions to the one-dimensional Schro¨dinger equation are possible only for particular discrete values of the total energy. Moreover, in the case of an electron in a well of atomic dimensions, the spacings between these energy levels are in qualitative agreement with the separations experimentally observed in atoms; we also interpreted the square of the wave function as a probability distribution for the position of the particle. These ideas led us to phenomena, such as quantum-mechanical tunnelling, that have been observed experimentally. The real world, however, is three-dimensional and, although one-dimensional examples often provide useful insights and analogies, we shall have to extend our theory into three dimensions before we can make quantitative predictions of most experimental results. In the present chapter, therefore, we shall set up the three-dimensional Schro¨dinger equation and obtain its solutions in a number of cases, culminating in a discussion of the hydrogen atom where we shall find that theory and experiment agree to a remarkable degree of accuracy.
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.
In the framework of the quantum model for hydrogen atom, we use the wave functions provided by the solutions of the Schrödinger equation with Coulomb potential. Considering the radial and angular densities of the localization probability, we identify the representative quantum states that play a high-probability role in transitions for H-I spectra. Besides that, we obtain some other complementary results. So, we present the numerical tables for the radial distributions, the electron density functions and some observables like θ nodal angles, nodal surfaces, along with the ordered sequences of the average radii in the sub-shells associated with this n: ⟨r⟩4f = 18a0 < ⟨r⟩4d = 21a0 < ⟨r⟩4p = 23a0 < ⟨r⟩4s = 24a0 (a0 - the first Bohr radius). Further, we have added the significant scientific 3D-visualization of the orbitals shapes and describe them via the nodal values for θ angles.
Featuring new coverage of quantum engineering and quantum information processing, the third edition of this bestselling textbook continues to provide a uniquely practical introduction to the fundamentals of quantum mechanics. It features straightforward explanations of quantum effects, suitable for readers from all backgrounds; real-world engineering problems showcasing the practical application of theory to practice, providing a relevant and accessible introduction to cutting-edge quantum applications; over 60 accessible worked examples using MATLAB (as well as open-source Python), allowing deepened understanding through computational exploration and visualization; and a new chapter on quantum engineering, introducing state-of-the-art concepts in quantum information processing and quantum device design. Updated throughout and supported online by downloadable MATLAB code, exam questions, and solutions to over 150 homework problems for instructors, this is the ideal textbook for senior undergraduate and graduate students in applied science, applied physics, engineering, and materials science studying a first course in quantum mechanics.