Original scientific paper

The quantum oscillator in phase space. Part I

Emile Grgin ; Institute Rudjer Bošković Zagreb, Croatia
Guido Sandri ; Boston University, 111 Cummington St. Boston, MA 02215

Abstract

Starting with a real abstract algebra which encapsulates the algebraic structures of both classical and quantum mechanics, this paper presents a self–contained realization of the latter in phase space. Having both mechanics formulated in the same space opens two new windows into the comparative study of foundations. This stems from the fact that the same physical problem, as defined by a given Hamiltonian, can be solved in several independent ways. The exact solutions can then be compared. Thus, comparison of the classical and quantum solutions in phase space offers new epistemological insights into Bohr’s correspondence principle, while comparison of the quantum solutions in the different formalisms of Hilbert space and phase space yields new physical insights. These general ideas are then tested on the harmonic oscillator. The analytic ground work is presented in Part I, the exact solutions will be derived in Part II.

Keywords

Hrčak ID:

303492

URI

https://hrcak.srce.hr/303492

Publication date:

1.7.1996.

Article data in other languages: croatian

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