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FIZIKA B 5 (1996) 3, 141-158
 
THE QUANTUM OSCILLATOR IN PHASE SPACE
Part I
EMILE GRGIN and GUIDO SANDRIa
Institute Rudjer Bošković Zagreb, Croatia
aBoston University, 111 Cummington St. Boston, MA 02215
Received 10 November 1995
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.
UDC 530.145
PACS 03.65.Ca
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