Quantization of a Hamiltonian system with an infinite number of degrees of freedom | Zendy

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Quantization of a Hamiltonian system with an infinite number of degrees of freedom

Author(s) -

Peter Zhidkov

Publication year - 1995

Publication title -

letters in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.915

H-Index - 62

eISSN - 1573-0530

pISSN - 0377-9017

DOI - 10.1007/bf00749684

Subject(s) - quantization (signal processing) , hamiltonian (control theory) , hamiltonian system , mathematics , degrees of freedom (physics and chemistry) , mathematical physics , infinity , finite set , classical mechanics , complex system , canonical quantization , quantum , quantum mechanics , physics , mathematical analysis , quantum gravity , computer science , mathematical optimization , artificial intelligence , algorithm

We propose a method of quantization of a discrete Hamiltonian system with an infinite number of degrees of freedom. Our approach is analogous to the usual finite-dimensional quantum mechanics. We construct an infinite-dimensional Schrödinger equation. We show that it is possible to pass from the finite-dimensional quantum mechanics to our construction in the limit when the number of particles tends to infinity. Rigorous mathematical methods are used.

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