Unique Structure of Free Particle Bound States

2016 ◽  
Vol 17 (6) ◽  
pp. 1-11
Author(s):  
Hans-Peter Morsch
Keyword(s):  
Bound States ◽  
Free Particle ◽  
Unique Structure

scholarly journals Solutions of the Relativistic Two-Body Problem. II. Quantum Mechanics

1972 ◽  
Vol 25 (2) ◽  
pp. 141 ◽  
Author(s):  
JL Cook
Keyword(s):  
Bound States ◽  
Free Particle ◽  
Plane Waves ◽  
Addition Theorem ◽  
Partial Wave Analysis ◽  
Harmonic Oscillator Potential ◽  
Two Body Problem ◽  
Probability Densities ◽  
Square Well ◽  
Potential Harmonic

This paper discusses the formulation of a quantum mechanical equivalent of the relative time classical theory proposed in Part I. The relativistic wavefunction is derived and a covariant addition theorem is put forward which allows a covariant scattering theory to be established. The free particle eigenfunctions that are given are found not to be plane waves. A covariant partial wave analysis is also given. A means is described of converting wavefunctions that yield probability densities in 4-space to ones that yield the 3-space equivalents. Bound states are considered and covariant analogues of the Coulomb potential, harmonic oscillator potential, inverse cube law of force, square well potential, and two-body fermion interactions are discussed.

scholarly journals A GENERAL SCHEME FOR THE EFFECTIVE-MASS SCHRÖDINGER EQUATION AND THE GENERATION OF THE ASSOCIATED POTENTIALS

2004 ◽  
Vol 19 (37) ◽  
pp. 2765-2775 ◽  
Author(s):  
B. BAGCHI ◽  
P. GORAIN ◽  
C. QUESNE ◽  
R. ROYCHOUDHURY
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Bound States ◽  
General Scheme ◽  
Free Particle ◽  
Energy Operator ◽  
Unified Approach ◽  
One Dimensional ◽  
Effective Mass Schrödinger Equation

A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.

A NEW GEOMETRICAL FRAMEWORK FOR THE DE BROGLIE–BOHM QUANTUM THEORY

2013 ◽  
Vol 10 (03) ◽  
pp. 1250096 ◽  
Author(s):  
D. J. HURLEY ◽  
M. A. VANDYCK
Keyword(s):  
Quantum Theory ◽  
Bound States ◽  
Particle System ◽  
Zeeman Effect ◽  
Free Particle ◽  
Physical Space ◽  
Quantization Condition ◽  
Curvilinear Coordinates ◽  
Dimensional Manifold ◽  
De Broglie Bohm

A geometrical framework for the de Broglie–Bohm quantum theory is presented, in which the trajectories of an N-particle system are interpretable as the integral curves of a particular vector field defined on a 3N-dimensional manifold [Formula: see text] constructed from physical space M. It is mathematically valid even when M is curved. If M is flat, the usual theory is recovered and automatically expressed in whatever curvilinear coordinates one may wish to choose. The general construction is illustrated by the case of a free particle moving on the surface of a sphere. (A modified Bohr quantization condition for angular momentum is obtained, with a first correction proportional to the curvature.) The Zeeman effect and some bound states on the sphere are also considered.

Recent Radiative and Collisional Atomic Data of Astrophysical Interest

1988 ◽  
Vol 102 ◽  
pp. 129-132
Author(s):  
K.L. Baluja ◽  
K. Butler ◽  
J. Le Bourlot ◽  
C.J. Zeippen
Keyword(s):  
Mass Production ◽  
Bound States ◽  
Physical Models ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Atomic Data ◽  
Isoelectronic Sequence ◽  
Astrophysical Interest ◽  
Radiative Transitions ◽  
Forbidden Transitions

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.

Spectrum of Bound States of Nucleus 10B in a Three-Cluster Microscopic Model

2014 ◽  
Vol 59 (11) ◽  
pp. 1065-1077 ◽  
Author(s):  
A.V. Nesterov ◽  
◽  
V.S. Vasilevsky ◽  
T.P. Kovalenko ◽  
◽  
...  
Keyword(s):  
Bound States ◽  
Microscopic Model

Relationship Between Level of Income and Method of Contribution and Appointment of Islamic Waqf Bank as an Agent in Collecting Waqf Fund

2014 ◽  
Vol 2 (2) ◽  
pp. 15
Author(s):  
Muhammad Ridhwan Ab. Aziz ◽  
Mohd Asyraf Yusof ◽  
Fuadah Johari ◽  
Hisham Sabri
Keyword(s):  
Support Services ◽  
Quantitative Research ◽  
Financial Institution ◽  
The Other ◽  
Strong Tendency ◽  
Trust Fund ◽  
Cost Of Living ◽  
Good Education ◽  
Unique Structure ◽  
The Relationship

Receiving a good education helps empower people knowledge, thus making them strong enough to look after themselves in any given situation. It keeps oneself aware of given surrounding as well as the rules and regulations of the society they living in. Moreover, the technology that we use today is a result from the advancement and improvement of education. On the other hand Islamic waqf bank is a special designed financial institution in Islam. This bank will benefit the student and also their parents, due to its unique structure that could finance students‟ education in term of fees and cost of living. Islamic waqf bank uses the concept of cash waqf in terms of funding the education. While cash waqf is a trust fund established with money to support services for mankind‟s benefits in the name of Allah. The objective of this article is to examine the relationship between level of income and contribution method of cash waqf fund in Islamic waqf bank as well as the appointment of an agent in collecting waqf fund in Islamic waqf bank. The methodology of this research is a quantitative research towards 287 respondents among Muslim public in this country. The general finding of this article shows that, with proper contribution method and the appointment of Islamic waqf bank as an agent in collecting the cash waqf fund, there is a strong tendency that the Islamic waqf bank‟s operation will be run effectively.

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