The Bohm quantum potential and the classical limit of quantum mechanics

2003 ◽  
Vol 81 (7) ◽  
pp. 971-976 ◽  
Author(s):  
A O Bolivar
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit ◽  
Quantum Potential ◽  
Limit Formula ◽  
Bohm Quantum Potential

Using a procedure based on the limit [Formula: see text], we show that the classical limiting method based on the Bohm quantum potential (Q [Formula: see text] 0) is not necessary to characterize the classical limit of quantum mechanics. PACS No.: 03.65.Ta

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.

A Critique of the Classical Limit Problem of Quantum Mechanics

2006 ◽  
Vol 19 (5) ◽  
pp. 403-421 ◽  
Author(s):  
D. Sen ◽  
S. Sengupta
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit ◽  
Limit Problem

q-Equivalent Hamiltonian Operators

1972 ◽  
Vol 50 (17) ◽  
pp. 2037-2047 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit ◽  
First Integral ◽  
Canonical Commutation Relation ◽  
Equation Of Motion ◽  
First Integrals ◽  
Position Operator ◽  
Integrals Of Motion ◽  
Adjoint Operators ◽  
Hamiltonian Operators

From the equation of motion and the canonical commutation relation for the position of a particle and its conjugate momentum, different first integrals of motion can be constructed. In addition to the proper Hamiltonian, there are other operators that can be considered as the generators of motion for the position operator (q-equivalent Hamiltonians). All of these operators have the same classical limit for the probability density of the coordinate of the particle, and many of them are symmetric and self-adjoint operators or have self-adjoint extensions. However, they do not satisfy the Heisenberg rule of quantization, and lead to incorrect commutation relations for velocity and position operators. Therefore, it is concluded that the energy first integral and the potential, rather than the equation of motion and the force law, are the physically significant operators in quantum mechanics.

On the Completeness of the Classical Limit of Quantum Mechanics

1992 ◽  
pp. 241-248
Author(s):  
Giorgio Mantica ◽  
Joseph Ford
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit

scholarly journals Path Integrals, Spontaneous Localisation, and the Classical Limit

2020 ◽  
Vol 75 (2) ◽  
pp. 131-141 ◽  
Author(s):  
Bhavya Bhatt ◽  
Manish Ram Chander ◽  
Raj Patil ◽  
Ruchira Mishra ◽  
Shlok Nahar ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Path Integral ◽  
Classical Limit ◽  
Measurement Problem ◽  
Path Integrals ◽  
Path Integral Formulation ◽  
Von Neumann ◽  
Matrix Evolution ◽  
Grw Model

AbstractThe measurement problem and the absence of macroscopic superposition are two foundational problems of quantum mechanics today. One possible solution is to consider the Ghirardi–Rimini–Weber (GRW) model of spontaneous localisation. Here, we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. We provide two new pedagogical derivations of the GRW propagator. We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral.

scholarly journals The Equivalence Postulate of Quantum Mechanics, Dark Energy, and the Intrinsic Curvature of Elementary Particles

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Alon E. Faraggi
Keyword(s):  
Quantum Mechanics ◽  
Dark Energy ◽  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Schrodinger Equation ◽  
Axiomatic Approach ◽  
Quantum Potential ◽  
Curvature Term ◽  
Cocycle Condition ◽  
Hamilton Jacobi Equation

The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underlie the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant underD-dimensional Möbius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of theD-dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrödinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. The author proposes that the quantum potential, which is always nontrivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multiparticle case the quantum potential, as well as the mass, is cumulative.

Exact classical limit of quantum mechanics: Central potentials and specific states

2002 ◽  
Vol 65 (3) ◽  
Author(s):  
Adam J. Makowski
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit
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