Properties of One-Dimensional Correlated Gaussian Wave Functions

1966 ◽  
Vol 141 (1) ◽  
pp. 281-286 ◽  
Author(s):  
T. R. Koehler
Keyword(s):  
Wave Functions ◽  
One Dimensional

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

scholarly journals DISTRIBUTION OF MAXIMA OF THE ANTISYMMETRIZED WAVE FUNCTION FOR THE NUCLEONS OF A CLOSED-SHELL AND FOR THE NUCLEONS OF ALL CLOSED-SHELLS IN A NUCLEUS.

2020 ◽  
Vol 15 ◽  
pp. 57
Author(s):  
G. S. Anagnostatos
Keyword(s):  
Wave Function ◽  
Mathematical Problem ◽  
Closed Shell ◽  
Wave Functions ◽  
Pictorial Representation ◽  
One Dimensional ◽  
Regular Polyhedra ◽  
Closed Shell Nuclei ◽  
Simple Systems ◽  
Closed Shells

The significant features of exchange symmetry are displayed by simple systems such as two identical, spinless fermions in a one-dimensional well with infinite walls. The conclusion is that the maxima of probability of the antisymmetrized wave function of these two fermions lie at the same positions as if a repulsive force (of unknown nature) was applied between these two fermions. This conclusion is combined with the solution of a mathematical problem dealing with the equilibrium of identical repulsive particles (of one or two kinds) on one or more spheres like neutrons and protons on nuclear shells. Such particles are at equilibrium only for specific numbers of particles and, in addition, if these particles lie on the vertices of regular polyhedra or their derivative polyhedra. Finally, this result leads to a pictorial representation of the structure of all closed shell nuclei. This representation could be used as a laboratory for determining nuclear properties and corresponding wave functions.

scholarly journals SPIN – A Schrödinger-Poisson Solver Including Nonparabolic Bands

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 489-493
Author(s):  
H. Kosina ◽  
C. Troger
Keyword(s):  
Dispersion Relation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Two Dimensional ◽  
Electron Systems ◽  
Dimensional Electron ◽  
One Dimensional ◽  
Poisson Solver ◽  
Two Dimensional Electron Systems

Nonparabolicity effects in two-dimensional electron systems are quantitatively analyzed. A formalism has been developed which allows to incorporate a nonparabolic bulk dispersion relation into the Schrödinger equation. As a consequence of nonparabolicity the wave functions depend on the in-plane momentum. Each subband is parametrized by its energy, effective mass and a subband nonparabolicity coefficient. The formalism is implemented in a one-dimensional Schrödinger-Poisson solver which is applicable both to silicon inversion layers and heterostructures.

Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions

2012 ◽  
Vol 11 (3) ◽  
pp. 951-984 ◽  
Author(s):  
Dongsheng Yin ◽  
Chunxiong Zheng
Keyword(s):  
Fourier Transform ◽  
Coherent States ◽  
Numerical Experiments ◽  
Wave Length ◽  
Wave Functions ◽  
Parameter Recovery ◽  
Characteristic Wave ◽  
One Dimensional ◽  
Windowed Fourier Transform ◽  
Recovery Algorithm

AbstractThe coherent states approximation for one-dimensional multi-phased wave functions is considered in this paper. The wave functions are assumed to oscillate on a characteristic wave length 0(ε) with ε ≪ 1. A parameter recovery algorithm is first developed for single-phased wave function based on a moment asymptotic analysis. This algorithm is then extended to multi-phased wave functions. If cross points or caustics exist, the coherent states approximation algorithm based on the parameter recovery will fail in some local regions. In this case, we resort to the windowed Fourier transform technique, and propose a composite coherent states approximation method. Numerical experiments show that the number of coherent states derived by the proposed method is much less than that by the direct windowed Fourier transform technique.

scholarly journals On the Nature of Electronic Wave Functions in One-Dimensional Self-Similar and Quasiperiodic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-35 ◽  
Author(s):  
Enrique Maciá
Keyword(s):  
Transport Properties ◽  
Wave Functions ◽  
Critical States ◽  
One Dimensional ◽  
Precise Nature ◽  
Self Similar ◽  
Electronic Wave Functions ◽  
Quasiperiodic Systems ◽  
The Relationship ◽  
Singular Continuous Spectra

The interest in the precise nature of critical states and their role in the physics of aperiodic systems has witnessed a renewed interest in the last few years. In this work we present a review on the notion of critical wave functions and, in the light of the obtained results, we suggest the convenience of some conceptual revisions in order to properly describe the relationship between the transport properties and the wave functions distribution amplitudes for eigen functions belonging to singular continuous spectra related to both fractal and quasiperiodic distribution of atoms through the space.

Collective motion in the nuclear shell model III. The calculation of spectra

1963 ◽  
Vol 272 (1351) ◽  
pp. 557-577 ◽  
Keyword(s):  
Shell Model ◽  
Collective Motion ◽  
Mass Region ◽  
Wave Functions ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
One Dimensional ◽  
The One ◽  
Nuclear Shell ◽  
Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

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