Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Betascript Publishing eBooks

Perturbation theory : Quantum mechanics, perturbation theory quantum mechanics, power series, orbit of the moon, Newton's laws of motion, numerical analysis

Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow

Published Jan 1, 2011• 0 citations
OpenAlex

Related papers

From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

A. Bouda

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a nonrelativistic spinless system. This Lagrangian is written as a difference between a function T, which represents the quantum generalization of the kinetic energy and which depends on the coordinate x and the temporal derivatives of x up the third order, and the classical potential V(x). The Hamiltonian is then constructed and the corresponding canonical equations are deduced. The function T is first assumed to be arbitrary. The development of T in a power series together with the dimensional analysis allow us to fix univocally the series coefficients by requiring that the well-known quantum stationary Hamilton–Jacobi equation be reproduced. As a consequence of this approach, we formulate the law of the quantum motion representing a new version of the quantum Newton law. We also analytically establish the famous Bohm relation [Formula: see text] outside the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, plays really the role of an additional potential as assumed by Bohm.

arXiv:quant-ph/0210193•International Journal of Modern Physics A•Jul 30, 2003•20 citations

Perturbation Theory in Quantum Mechanics

Luigi E. Picasso, L. Bracci, Emilio d’Emilio

Springer eBooks•Oct 19, 2011•1 citation

Three-Part Invention

Michael G. Munowitz

The Moon — caught in an exact balance of attractive and repulsive forces — orbits the Earth with flawless regularity, never faltering. A ball rolls predictably down a slope of a certain grade, always passing the same landmarks in the same sequence of times. There are no surprises in the macroscopic world of classical mechanics, a world where to know the present is to predict the future and retrace the past. Observations may differ superficially according to individual frames of reference, but there is always agreement on the larger issues. Energy is conserved. Momentum is conserved. Differences in coordinates and velocities, along with perceptions of motion and rest, are all reconciled, and Newton’s deterministic equations of motion are the law of the land.

Oxford University Press eBooks•Jan 12, 2006•0 citations

Mathematical Fundamentals of Perturbation Theory

C. Vargas‐Hernández

Springer eBooks•Jan 1, 2025•0 citations

Perturbation Theory in Quantum Mechanics

CRC Press eBooks•Sep 19, 2000•2 citations

Limitations Of Newton's Second Law In The Quantum Realm: A Comparative Analysis With Quantum Physics

Balakrishna M.T

Newton's second law of motion, F = ma, has long been considered a cornerstone of classical mechanics, providing a fundamental framework for understanding the behavior of macroscopic objects. However, as physics delves into the quantum realm, the applicability of Newton's second law becomes limited, and the principles of quantum mechanics emerge as the dominant description of particle behavior. Beginning with an overview of the historical development of classical mechanics by Newton and the emergence of quantum mechanics in the early 20th century, the article delves into the foundational principles of framework. The classical description of particles as point masses with deterministic trajectories is contrasted with the probabilistic nature of quantum particles described by wave functions and superposition principles. Practical applications and implications of these theories are also discussed, shedding light on their significance in various scientific disciplines. This research article presents a comparative analysis of Newton's second law of motion and quantum physics, examining their fundamental principles and implications through the lens of classical and quantum mechanics. Beginning with an overview of Newton's second law and its significance in classical mechanics, the article delves into the foundational postulates of quantum mechanics and their departure from classical concepts. This explores the inherent limitations of Newton's second law when applied to quantum phenomena, comparing and contrasting its principles with those of quantum physics. Through a comprehensive analysis of evidence and theoretical frameworks, this article elucidates the boundaries of classical mechanics and highlights the need for quantum mechanics to describe phenomena at the atomic and subatomic levels. Through an exploration of key differences and similarities, this aims to provide insights into the behavior of particles at both macroscopic and microscopic scales

Educational Administration Theory and Practice journal•Apr 4, 2024•0 citations
In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a nonrelativistic spinless system. This Lagrangian is written as a difference between a function T, which represents the quantum generalization of the kinetic energy and which depends on the coordinate x and the temporal derivatives of x up the third order, and the classical potential V(x). The Hamiltonian is then constructed and the corresponding canonical equations are deduced. The function T is first assumed to be arbitrary. The development of T in a power series together with the dimensional analysis allow us to fix univocally the series coefficients by requiring that the well-known quantum stationary Hamilton–Jacobi equation be reproduced. As a consequence of this approach, we formulate the law of the quantum motion representing a new version of the quantum Newton law. We also analytically establish the famous Bohm relation [Formula: see text] outside the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, plays really the role of an additional potential as assumed by Bohm.
The Moon — caught in an exact balance of attractive and repulsive forces — orbits the Earth with flawless regularity, never faltering. A ball rolls predictably down a slope of a certain grade, always passing the same landmarks in the same sequence of times. There are no surprises in the macroscopic world of classical mechanics, a world where to know the present is to predict the future and retrace the past. Observations may differ superficially according to individual frames of reference, but there is always agreement on the larger issues. Energy is conserved. Momentum is conserved. Differences in coordinates and velocities, along with perceptions of motion and rest, are all reconciled, and Newton’s deterministic equations of motion are the law of the land.
Newton's second law of motion, F = ma, has long been considered a cornerstone of classical mechanics, providing a fundamental framework for understanding the behavior of macroscopic objects. However, as physics delves into the quantum realm, the applicability of Newton's second law becomes limited, and the principles of quantum mechanics emerge as the dominant description of particle behavior. Beginning with an overview of the historical development of classical mechanics by Newton and the emergence of quantum mechanics in the early 20th century, the article delves into the foundational principles of framework. The classical description of particles as point masses with deterministic trajectories is contrasted with the probabilistic nature of quantum particles described by wave functions and superposition principles. Practical applications and implications of these theories are also discussed, shedding light on their significance in various scientific disciplines. This research article presents a comparative analysis of Newton's second law of motion and quantum physics, examining their fundamental principles and implications through the lens of classical and quantum mechanics. Beginning with an overview of Newton's second law and its significance in classical mechanics, the article delves into the foundational postulates of quantum mechanics and their departure from classical concepts. This explores the inherent limitations of Newton's second law when applied to quantum phenomena, comparing and contrasting its principles with those of quantum physics. Through a comprehensive analysis of evidence and theoretical frameworks, this article elucidates the boundaries of classical mechanics and highlights the need for quantum mechanics to describe phenomena at the atomic and subatomic levels. Through an exploration of key differences and similarities, this aims to provide insights into the behavior of particles at both macroscopic and microscopic scales