ONE DIMENSIONAL SCATTERING PROBLEM IN BOHMIAN QUANTUM MECHANICS

2009 ◽  
Vol 07 (05) ◽  
pp. 1029-1038
Author(s):  
S. MOHAMMADI
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Scattering Problem ◽  
Additional Element ◽  
Standard Quantum ◽  
Quantum Tunnelling ◽  
Barrier Heights ◽  
Bohmian Quantum Mechanics ◽  
Bohmian Interpretation ◽  
De Broglie Bohm

According to Standard Quantum Mechanics (SQM), known as the Copenhagen Interpretation, the complete description of a system of particles is provided by its wave function. However, in the de Broglie-Bohm theory of Bohmian Quantum Mechanics (BQM), the additional element which is introduced apart from the wave function is the particle position, conceived in the classical sense as pursuing a definite continuous track in space-time. In BQM formulation, depending on the configuration of the potential barrier and the energy of the packet, the particle trajectories have been shown to take distinct paths. We will consider several barrier heights and show that in a Bohmian interpretation of the problem, there is no such thing as Quantum Tunnelling.

scholarly journals Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function

2020 ◽  
Author(s):  
Shuming Wen
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Physical Mechanism ◽  
Theoretical Expression ◽  
Quantum Tunnelling ◽  
Tunnelling Effect ◽  
Physical Particle ◽  
Objective System ◽  
Energy Quantum ◽  
Definition Of

Abstract The theoretical calculation of quantum mechanics has been accurately verified by experiments, but Copenhagen interpretation with probability is still controversial. To find the source of the probability, we revised the definition of the energy quantum and reconstructed the wave function of the physical particle. Here, we found that the energy quantum ê is 6.62606896 ×10-34J instead of hν as proposed by Planck. Additionally, the value of the quality quantum ô is 7.372496 × 10-51 kg. This discontinuity of energy leads to a periodic non-uniform spatial distribution of the particles that transmit energy. A quantum objective system (QOS) consists of many physical particles whose wave function is the superposition of the wave functions of all physical particles. The probability of quantum mechanics originates from the distribution rate of the particles in a state in the QOS per unit volume at time t and near position r. Based on the revision of the energy quantum assumption and the origin of the probability, we proposed new certainty and uncertainty relationships, explained the physical mechanism of wave-function collapse and the quantum tunnelling effect, derived the quantum theoretical expression of double-slit and single-slit experiments.

TOPOLOGICAL SOLUTION OF BOHMIAN QUANTUM MECHANICS

2009 ◽  
Vol 24 (06) ◽  
pp. 453-461 ◽  
Author(s):  
XUGUANG SHI ◽  
MING YU ◽  
YISHI DUAN
Keyword(s):  
Quantum Mechanics ◽  
Particle System ◽  
World Line ◽  
Zero Point ◽  
Current Theory ◽  
Brouwer Degree ◽  
Topological Current ◽  
The World ◽  
Bohmian Quantum Mechanics ◽  
De Broglie Bohm

The topological solutions of the De Broglie–Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ϕ-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.

An experiment for testing de Broglie — Bohm theory against standard quantum mechanics

2003 ◽  
pp. 459-459
Author(s):  
G. Brida ◽  
M. Genovese ◽  
C. Novero ◽  
G. Introzzi ◽  
P. Ghose ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Standard Quantum ◽  
De Broglie Bohm

Localization of a bound particle outside the potential well

2002 ◽  
Vol 80 (7) ◽  
pp. 755-766 ◽  
Author(s):  
R F Holub ◽  
P K Smrz
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Effect ◽  
Energy State ◽  
Potential Well ◽  
Zero Energy ◽  
Standard Quantum ◽  
Simple Effect ◽  
The Common

We describe a simple effect predicted by standard quantum mechanics concerning a particle bound in a potential well brought to the zero-energy state by deformation of the well. When the effect takes place within a crack with impermeable walls the probability of localization of the particle reaches its maximum near the end of the crack. The wave function describing the bound particle may thus decohere far from the potential well. There are numerous instances of experimental data, gathered mostly by geochemists and other scientists over the last several decades, that are anomalous and defy all attempts to explain them by means of classical chemistry and physics. The common attribute of these data is a strange transport of particles over large distances that may be caused by the quantum effect described in the first part of the paper. The motivation for writing this paper is our hope to stimulate interest and critical testing of such an hypothesis. PACS Nos.: 03.65, 82.90, 91.90

scholarly journals Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function

2020 ◽  
Author(s):  
Shuming Wen
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Physical Mechanism ◽  
Theoretical Expression ◽  
Quantum Tunnelling ◽  
Tunnelling Effect ◽  
Physical Particle ◽  
Objective System ◽  
Energy Quantum ◽  
Definition Of

Abstract The theoretical calculation of quantum mechanics has been accurately verified by experiments, but Copenhagen interpretation with probability is still controversial. To find the source of the probability, we revised the definition of the energy quantum and reconstructed the wave function of the physical particle. Here, we found that the energy quantum ê is 6.62606896 ×10-34J instead of hν as proposed by Planck. Additionally, the value of the quality quantum ô is 7.372496 × 10-51 kg. This discontinuity of energy leads to a periodic non-uniform spatial distribution of the particles that transmit energy. A quantum objective system (QOS) consists of many physical particles whose wave function is the superposition of the wave functions of all physical particles. The probability of quantum mechanics originates from the distribution rate of physical particles in a state in the QOS per unit volume at time t and near position r. Based on the revision of the energy quantum assumption and the origin of the probability, we proposed new certainty and uncertainty relationships, explained the physical mechanism of wave-function collapse and the quantum tunnelling effect, derived the quantum theoretical expression of double-slit and single-slit experiments.

scholarly journals Quantum and Classical Cosmology in the Brans–Dicke Theory

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 286
Author(s):  
Carla R. Almeida ◽  
Olesya Galkina ◽  
Julio César Fabris
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Classical Model ◽  
Bohmian Mechanics ◽  
Finite Energy ◽  
Energy Conditions ◽  
Interpretation Of Quantum Mechanics ◽  
Expectation Values ◽  
Bohm Interpretation ◽  
De Broglie Bohm

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω<−32, the energy is bounded from below and singularity-free solutions are found. However, in the case ω>−32, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of ω.

THE SHADOW OF LIGHT: CHALLENGING CLASSICAL AND QUANTUM ELECTRODYNAMICS

2007 ◽  
Vol 21 (26) ◽  
pp. 4437-4471 ◽  
Author(s):  
FABIO CARDONE ◽  
ROBERTO MIGNANI
Keyword(s):  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Lorentz Invariance ◽  
Anomalous Behavior ◽  
Copenhagen Interpretation ◽  
Threshold Behavior ◽  
Standard Quantum ◽  
Pilot Wave ◽  
Bohmian Quantum Mechanics ◽  
Local Lorentz Invariance

We review some optical experiments, carried out in the last decade, which evidence an anomalous behavior of photon systems. Their results are apparently at variance with both standard quantum mechanics (in the Copenhagen interpretation) and usual (classical and quantum) electrodynamics. In particular, they can be interpreted as a virtual interference involving the pilot waves associated to photons (according to Bohmian quantum mechanics). The anomalous effects exhibit a threshold behavior in energy and space, which agrees with results obtained on the electromagnetic breakdown of local Lorentz invariance. A possible connection between these seemingly unrelated implications of the observed phenomenon can be set by assuming that the pilot wave of a photon is a deformation of spacetime ("shadow of light").

scholarly journals Gravitational reduction of the wave function based on Bohmian quantum potential

2018 ◽  
Vol 33 (22) ◽  
pp. 1850129
Author(s):  
Faramarz Rahmani ◽  
Mehdi Golshani ◽  
Ghadir Jafari
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Classical Limit ◽  
Free Particle ◽  
Bohmian Mechanics ◽  
Quantum Potential ◽  
Interesting Connection ◽  
Bohmian Quantum Mechanics ◽  
Usual Criterion ◽  
Quantum Force

In objective gravitational reduction of the wave function of a quantum system, the classical limit of the system is obtained in terms of the objective properties of the system. On the other hand, in Bohmian quantum mechanics the usual criterion for getting classical limit is the vanishing of the quantum potential or the quantum force of the system, which suffers from the lack of an objective description. In this regard, we investigated the usual criterion of getting the classical limit of a free particle in Bohmian quantum mechanics. Then we argued how it is possible to have an objective gravitational classical limit related to the Bohmian mechanical concepts like quantum potential or quantum force. Also we derived a differential equation related to the wave function reduction. An interesting connection will be made between Bohmian mechanics and gravitational concepts.

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