scholarly journals SYMPLECTIC STRUCTURES AND QUANTUM MECHANICS

1996 ◽  
Vol 10 (12) ◽  
pp. 545-553 ◽  
Author(s):  
GIUSEPPE MARMO ◽  
GAETANO VILASI
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Classical Field Theory ◽  
General Setting ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Starting Point ◽  
Good Starting Point ◽  
Von Neumann Theorem

Canonical coordinates for the Schrödinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schrödinger equation, considered as a classical field theory, shares with Liouville completely integrable field theories the existence of a recursion operator which allows for the infinitely many conserved functionals pairwise commuting with respect to the corresponding Poisson bracket. The approach may provide a good starting point to get a clear interpretation of Quantum Mechanics in the general setting, provided by Stone–von Neumann theorem, of Symplectic Mechanics. It may give new tools to solve in the general case the inverse problem of quantum mechanics whose solution is given up to now only for one-dimensional systems by the Gel’fand-Levitan-Marchenko formula.

GEODESIC FLOWS, VON NEUMANN EQUATION AND QUANTUM MECHANICS ON NONCOMMUTATIVE CYLINDER

2006 ◽  
Vol 21 (28) ◽  
pp. 2151-2160
Author(s):  
PARTHA GUHA
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Geodesic Flows ◽  
Von Neumann ◽  
Discrete Schrödinger Equation ◽  
Von Neumann Equation ◽  
Area Preserving

We study quantum mechanics on the noncommutative cylinder via Moyal deformed geodesic flows on the group of area preserving diffeomorphism. This equation coincides exactly with the von Neumann equation. Using discretization techniques of Kemmoku and Saito we obtain the discrete Schrödinger equation on noncommutative cylinder. Thus we reproduce the result of Balachandran et al.1

scholarly journals On the categoricity of quantum mechanics

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Iulian D. Toader
Keyword(s):  
Quantum Mechanics ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Von Neumann Theorem

AbstractThe paper offers an argument against an intuitive reading of the Stone-von Neumann theorem as a categoricity result, thereby pointing out that, against what is usually taken to be the case, this theorem does not entail any model-theoretical difference between the theories that validate it and those that don’t.

scholarly journals Topological dynamics and ergodic theory

1987 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
Robert Ellis
Keyword(s):  
Discrete Spectrum ◽  
Ergodic Theory ◽  
General Setting ◽  
Topological Dynamics ◽  
Von Neumann ◽  
Ergodic Processes ◽  
Neumann Theorem ◽  
Von Neumann Theorem

AbstractIt is shown that when viewed properly some concepts in topological dynamics and ergodic theory are not merely analogous but equivalent. Also the Mackey-Halmos-von Neumann theorem on ergodic processes with discrete spectrum is generalized and an account of the Mackey-Zimmer theory of minimal cocycles is given in a more general setting.

scholarly journals QUANTUM GROUPS AND VON NEUMANN THEOREM

1994 ◽  
Vol 08 (04) ◽  
pp. 269-276 ◽  
Author(s):  
ALFREDO IORIO ◽  
GIUSEPPE VITIELLO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Quantum Field ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Von Neumann Theorem ◽  
Inequivalent Representations

We discuss the q-deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in quantum mechanics. We show that the q-deformation parameter labels the Weyl systems in quantum mechanics and the unitarily inequivalent representations of the canonical commutation relations in quantum field theory.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

scholarly journals When does the Weyl-von Neumann Theorem hold?

2017 ◽  
Vol 49 (4) ◽  
pp. 742-744
Author(s):  
Hiroshi Ando ◽  
Yasumichi Matsuzawa
Keyword(s):  
Von Neumann ◽  
Neumann Theorem ◽  
Von Neumann Theorem

A Student's Guide to the Schrödinger Equation

2020 ◽  
Author(s):  
Daniel A. Fleisch
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Plain Language ◽  
Science And Engineering ◽  
Popular Approach ◽  
Matlab Code ◽  
Mathematical Techniques

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.

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