scholarly journals Self-consistent and environment-dependent Hamiltonian for quantum-mechanics materials simulations.

2007 ◽  
Author(s):  
Christopher Leahy
Keyword(s):  
Quantum Mechanics ◽  
Self Consistent

scholarly journals The Enigma of the Muon and Tau Solved by Emergent Quantum Mechanics?

2019 ◽  
Vol 9 (7) ◽  
pp. 1471
Author(s):  
Theo van Holten
Keyword(s):  
Quantum Mechanics ◽  
Droplet Model ◽  
Matter Waves ◽  
Equilibrium Configurations ◽  
Self Consistent ◽  
Usual Quantum ◽  
Electron Models ◽  
Charged Leptons ◽  
Emergent Quantum Mechanics

This paper addresses the long-standing question of how it may be explained that the three charged leptons (the electron, muon and tau particle) have different masses, despite their conformity in other respects. In the field of Emergent Quantum Mechanics non-singular electron models are being revisited, and from this exploration has come a possible answer. In this paper a deformable droplet model is considered. It is shown how the model can be made self-consistent, whilst obeying the laws of momentum and energy conservation as well as Larmor’s radiation law. The droplet appears to have three different static equilibrium configurations, each with a different mass. Tentatively, these three equilibrium masses were assumed to correspond with the measured masses of the charged leptons. The droplet model was tuned accordingly, and was thereby completely quantified. The dynamics of the droplet then showed a “De Broglie-like” relation p = K / λ . Beat patterns in the vibrations of the droplet play the role of the matter waves of usual quantum mechanics. The value of K , calculated by the droplet theory, practically equals Planck’s constant: K ≅ h . This fact seems to confirm the correctness of identifying the three types of charged leptons with the equilibria of a droplet of charge.

NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION II: NONSTATIONARY SITUATION

1993 ◽  
Vol 08 (16) ◽  
pp. 2683-2707 ◽  
Author(s):  
A. D. POPOVA ◽  
A. N. PETROV
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Variational Principles ◽  
Gravitational Interaction ◽  
Classical Field Theory ◽  
Classical Field ◽  
Stationary Case ◽  
Self Consistent ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

Quantum mechanics (first quantization) with self-consistent gravitational interaction, previously constructed for the stationary case, is extended to the general case. The two requirements for such a theory are realized: to obtain the theory maximally resembling a classical field theory and to achieve the invariance of the theory under the rescaling transformations of a wave function. The construction is not trivial, because it rejects the variational principles of extremality of any action and involves some principles of smoothed extremality which give relevant equations.

scholarly journals SCALING OF VARIABLES AND THE RELATION BETWEEN NONCOMMUTATIVE PARAMETERS IN NONCOMMUTATIVE QUANTUM MECHANICS

2006 ◽  
Vol 21 (10) ◽  
pp. 795-802 ◽  
Author(s):  
O. BERTOLAMI ◽  
J. G. ROSA ◽  
C. M. L. DE ARAGÃO ◽  
P. CASTORINA ◽  
D. ZAPPALÀ
Keyword(s):  
Quantum Mechanics ◽  
The Self ◽  
Effective Parameters ◽  
Noncommutative Algebra ◽  
Noncommutative Quantum Mechanics ◽  
Self Consistent ◽  
Limited Applicability ◽  
Direct Proportionality ◽  
Space Noncommutativity ◽  
Noncommutative Quantum

We consider noncommutative quantum mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.

scholarly journals Breve argumentación didáctica de la mecánica cuántica de muchos cuerpos

Respuestas ◽  
2017 ◽  
Vol 22 (1) ◽  
pp. 29
Author(s):  
Cristian Andrés Aguirre-Téllez ◽  
José Barba-Ortega
Keyword(s):  
Quantum Mechanics ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Analytical Method ◽  
Schrodinger Equation ◽  
Quantum Systems ◽  
The Self ◽  
Self Consistent ◽  
El Sistema ◽  
Self Consistent Field

El problema general en mecánica cuántica está basado en la solución de una ecuación en valores propios de un operador dado (en una representación adecuada), generalmente  dicho operador es el Hamiltoniano que da cuenta de la interacción energética (salvo que dependa del tiempo) del sistema en cuestión. La solución de la ecuación de Schrödinger permite escribir el comportamiento dinámico del sistema sometido a ciertas restricciones. Sin embargo, la solución analítica de esta ecuación es viable solo en sistemas simples, cuando el sistema se describe desde la interacción de muchas partículas (problema electrónico-base de la construcción de sistemas cuánticos complejos aplicable a la descripción de moléculas, sólidos y sistemas cuánticos interactuantes en general.) la solución de la ecuación de Schrödinger del sistema no se puede realizar vía método analítico; con lo cual existe una forma más global de enfrentar dicho problema, el método auto consistente; mediante el cual se puede solucionar sistemas complejos de muchos cuerpos. Es así que en el presente paper presentamos una comparación entre el sistema auto consistente y algunas variantes que existen, con el método analítico en sistemas demuchos cuerpos y como opera dicho método, esto aplicado a un problema de dos cuerpos con interacción Coulombiana, ya que este problema presenta solución analítica y ha sido extensamente estudiado; esto con la finalidad de que los estudiantes interesados en la materia comprendan como se abordan problemas vía métodos auto consistentes y como opera este método, ya que en la literatura pocas veces se presenta el algoritmo de solución mediante este método.Palabras clave: Mecánica Cuántica, Método Auto-Consistente, problema de dos cuerpos.AbstractThe general problem in quantum mechanics is based on the solution of an equation in eigenvalues of a given operator (in a suitable representation), generally said operator is the Hamiltonian that accounts for the energy interaction (unless it depends on the time) of the system in question. The solution of the Schrodinger equation allows writing the dynamic behavior of the system subject to certain restrictions. however, the analytical solution of this equation is feasible only in simple systems, when the system is described from the interaction of many particles (electronic problem- basis of the construction of complex quantum systems applicable to the description of molecules, solids and interacting quantum systems in general.), the solution of the Schrödinger equation of the system can´t be performed via analytical method; with which there is a more global way of facing this problem, the self-consistent method; through which complex systems of many bodies can be solved. thus, in the present paper we present a comparison between the self-consistent system and some variants that exist, with the analytical method in systems of many bodies and how this method operates, this applied to a problem of two bodies with Coulombian interaction, since this problem presents an analytical solution and has been extensively studied; this in order that students interested in the subject understand how problems are addressed through self-consistent methods and how this method operates, since in the literature rarely the solution algorithm is presented by this method.Keywords: Quantum mechanics, Self Consistent Field, Two body problem.

scholarly journals Self-consistent tomography and measurement-device independent cryptography

2020 ◽  
pp. 2040003
Author(s):  
I. D. Moore ◽  
S. J. van Enk
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
The State ◽  
Correlated Errors ◽  
Measurement Device ◽  
State Preparation ◽  
Self Consistent ◽  
Average State ◽  
Measurement Device Independent ◽  
Joint State

A recurring problem in quantum mechanics is to estimate either the state of a quantum system or the measurement operator applied to it. If we wish to estimate both, then the difficulty is that the state and the measurement always appear together: to estimate the state, we must use a measurement; to estimate the measurement operator, we must use a state. The data of such quantum estimation experiments come in the form of measurement frequencies. Ideally, the measured average frequencies can be attributed to an average state and an average measurement operator. If this is not the case, we have correlated state-preparation-and-measurement (SPAM) errors. We extend some tests developed to detect such correlated errors to apply to a cryptographic scenario in which two parties trust their individual states but not the measurement performed on the joint state.

A simple derivation of the quantum state from two assumptions

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180585
Author(s):  
Bo-Yu Sun
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Simple Derivation ◽  
The Real ◽  
Basic Assumptions ◽  
Born’S Rule ◽  
Self Consistent ◽  
Mathematical Foundations ◽  
Physical Principles ◽  
Real State

In this paper, based on the discussion on what the real state of a coin at each point should be, we propose two basic assumptions. Then we point out the mathematical foundations that these two assumptions rely on and the familiar physical principles which these two assumptions, respectively, correspond to. These two assumptions, as required, do not seek help from the well-known formulation of quantum mechanics. They are self-consistent in a new presentation. Based on two basic assumptions, we derive the real state in a simple way and claim that the real state equals the quantum state totally after comparison from different aspects. We thus prove that the quantum state is the ontological object which obeys the redefinition of the reality rather than just a vague concept in quantum theory. We also consider the way in which Born's rule arises naturally.

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