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

arXiv:quant-ph/0208021 · physica status solidi (b)

Wave Packets Can Factorize Numbers

H. Mack, M. Bienert, F. Haug, M. Freyberger, W.P. Schleich

Published Oct 1, 2002• 19 citations
arXivHTMLPDF

Abstract

We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.
DOI
10.1002/1521-3951(200210)233:3<408::aid-pssb408>3.0.co;2-n

Related papers

Wave Packets can Factorize Numbers

Holger Mack, Marc Bienert, Florian Haug +2 more

We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.

•Jan 1, 2002•20 citations

Wave packet dynamics and factorization of numbers

Holger Mack, Marc Bienert, Florian Haug +3 more

We connect three phenomena of wave packet dynamics: Talbot images, revivals of a particle in a box and fractional revivals. The physical origin of these effects is deeply rooted in phase factors which are quadratic in the quantum number. We show that the characteristic structures in the time evolution of these systems allow us to factorize large integers.

arXiv:quant-ph/0204040•Apr 8, 2002•2 citations

Factoring Numbers with Waves

Muhammad Suhail Zubairy

Finding prime factors of a number by means of wave interference may have applications in quantum computing and security systems.

Science•Apr 26, 2007•5 citations

Application of Grey System Theory in Approximate Calculation of Wave Packet Evolution

Jiayu Ni, Linfeng Ye, Gao, Dehong +1 more

The study of wave packet is of great significance in quantum mechanics, optics and fluid mechanics. However, in order to solve the strict evolution behavior of wave packet, it is necessary not only to determine the parameters of various physical quantities such as mass, but also to carry out the complex integration process in configuration space and momentum space. In the final analysis, the evolution behavior of wave packet is the evolution behavior of distribution function parameters with time. Using the method of grey system theory, the time-varying parameters are replaced by time-varying response series, and then the formal structure is constructed according to the physical meaning of time evolution to realize the approximate simulation and approximate calculation of wave function expression. The advantage of this method is that it can simulate the evolution of wave packet under the uncertainty of each physical quantity. Based on the grey system theory, this paper uses GM (1,1) model to replace the time response function of wave packet distribution, obtains the simulated evolution behavior of wave packet wave function by means of mathematical techniques such as variational method, and makes error analysis and correction. In practical application, the approximate evolution behavior of wave function can be obtained only by determining the parameters of expansion coefficient of wave function. In this paper, the Gauss wave packet is taken as an example to discuss the method. The grey system theory of mathematical modeling is introduced into physical calculation for the first time, and an approximate calculation method which can be widely used in wave packet evolution calculation is given.

arXiv:2104.04750•Apr 10, 2021•0 citations

Integers as a Key to Understanding Quantum Mechanics

Victor Korotkikh, Andrei Yu. Khrennikov

A description of complex systems based on integers is considered in the paper to suggest a new way of understanding quantum mechanics.

AIP conference proceedings•Jan 1, 2010•4 citations

Inverse problem of quadratic time-dependent Hamiltonians

Guangjie Guo, Yan Meng, Hong Chang +2 more

Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly.

Chinese Physics B•Aug 1, 2015•0 citations
The study of wave packet is of great significance in quantum mechanics, optics and fluid mechanics. However, in order to solve the strict evolution behavior of wave packet, it is necessary not only to determine the parameters of various physical quantities such as mass, but also to carry out the complex integration process in configuration space and momentum space. In the final analysis, the evolution behavior of wave packet is the evolution behavior of distribution function parameters with time. Using the method of grey system theory, the time-varying parameters are replaced by time-varying response series, and then the formal structure is constructed according to the physical meaning of time evolution to realize the approximate simulation and approximate calculation of wave function expression. The advantage of this method is that it can simulate the evolution of wave packet under the uncertainty of each physical quantity. Based on the grey system theory, this paper uses GM (1,1) model to replace the time response function of wave packet distribution, obtains the simulated evolution behavior of wave packet wave function by means of mathematical techniques such as variational method, and makes error analysis and correction. In practical application, the approximate evolution behavior of wave function can be obtained only by determining the parameters of expansion coefficient of wave function. In this paper, the Gauss wave packet is taken as an example to discuss the method. The grey system theory of mathematical modeling is introduced into physical calculation for the first time, and an approximate calculation method which can be widely used in wave packet evolution calculation is given.
Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly.