scholarly journals On the Boundary Conditions in Deformed Quantum Mechanics with Minimal Length Uncertainty

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Pouria Pedram
Keyword(s):  
Quantum Mechanics ◽  
Boundary Conditions ◽  
Adjoint Representation ◽  
Minimal Length ◽  
Wave Functions ◽  
Coordinate Space ◽  
Space Wave

We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint representation. We show how the boundary conditions in quasiposition space can be exactly determined from the boundary conditions in coordinate space.

scholarly journals Precision Measurement of the Position-Space Wave Functions of Gravitationally Bound Ultracold Neutrons

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Y. Kamiya ◽  
G. Ichikawa ◽  
S. Komamiya
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Bound States ◽  
Wave Functions ◽  
Recent Measurement ◽  
Ultracold Neutrons ◽  
Neutron Guide ◽  
Position Space ◽  
Position Sensitive Detectors ◽  
Space Wave

Gravity is the most familiar force at our natural length scale. However, it is still exotic from the view point of particle physics. The first experimental study of quantum effects under gravity was performed using a cold neutron beam in 1975. Following this, an investigation of gravitationally bound quantum states using ultracold neutrons was started in 2002. This quantum bound system is now well understood, and one can use it as a tunable tool to probe gravity. In this paper, we review a recent measurement of position-space wave functions of such gravitationally bound states and discuss issues related to this analysis, such as neutron loss models in a thin neutron guide, the formulation of phase space quantum mechanics, and UCN position sensitive detectors. The quantum modulation of neutron bound states measured in this experiment shows good agreement with the prediction from quantum mechanics.

scholarly journals The Minimal Length and the Shannon Entropic Uncertainty Relation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Pouria Pedram
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Commutation Relation ◽  
Deformation Parameter ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Adjoint Representation ◽  
Minimal Length ◽  
Entropic Uncertainty Relation ◽  
Ordinary Quantum

In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relationX,P=iħ1+βP2, whereβis the deformation parameter. Since the validity of the uncertainty relation for the Shannon entropies proposed by Beckner, Bialynicki-Birula, and Mycielski (BBM) depends on both the algebra and the used representation, we show that using the formally self-adjoint representation, that is,X=xandP=tan⁡βp/β, where[x,p]=iħ, the BBM inequality is still valid in the formSx+Sp≥1+ln⁡πas well as in ordinary quantum mechanics. We explicitly indicate this result for the harmonic oscillator in the presence of the minimal length.

scholarly journals DIFFRACTION EXPERIMENTS WITH KOSSEL PHOTONS

2021 ◽  
Vol 58 ◽  
pp. 3-10
Author(s):  
Oleg P. Nikotin ◽  
Keyword(s):  
Quantum Mechanics ◽  
Energy Resolution ◽  
Wave Functions ◽  
Coordinate Space ◽  
Diffraction Scattering ◽  
Sense Data ◽  
Space Experiments ◽  
Measurement Results ◽  
Angular Measurements ◽  
Spatial Parameters

In the paper an attempt was made to obtain some information about the characteristics of photons as separate objects with the properties of localization in ordinary coordinate space. Experiments of various complexity with Kossel photons were carried out on a multiaxial diffractometer. A diffraction spectrometer with perfect calcite crystals was used to register the photons. The bidirectional angular measurements were carried out with sufficient angular and energy resolution to detect the influence of the coherent volume of the photons on the measurement results. The measurements showed some correlations that had not been paid enough attention before. Those effects were measured separately for Kα1 and Kα2 photons to allow their comparison. Such approach corresponds to the modern quantum mechanics of the photon; that mechanics showed the possibility of existence of wave functions of photons in their usual standard sense. Data on spatial parameters Kα1 and Kα2 of Kossel photons were obtained by comparing the effects of their diffraction scattering

scholarly journals Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

2015 ◽  
Vol 70 (8) ◽  
pp. 619-627 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Hypergeometric Functions ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

AbstractWe consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

scholarly journals Quantum Mechanics in Metric Space: Wave Functions and Their Densities

2011 ◽  
Vol 106 (5) ◽  
Author(s):  
I. D’Amico ◽  
J. P. Coe ◽  
V. V. França ◽  
K. Capelle
Keyword(s):  
Quantum Mechanics ◽  
Metric Space ◽  
Wave Functions ◽  
Space Wave

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

A Student's Guide to the Schrödinger Equation

2020 ◽  
Author(s):  
Daniel A. Fleisch
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Plain Language ◽  
Science And Engineering ◽  
Popular Approach ◽  
Matlab Code ◽  
Mathematical Techniques

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.

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