Impossibility of naively generalizing squeezed coherent states

Journal Article · Thu Mar 15 00:00:00 EST 1984 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.29.1107· OSTI ID:6810511

Fisher, R A; Nieto, M M; Sandberg, V D

Pertinent properties of the unitary operators that create coherent states and squeezed coherent states are discussed. We show that certain generalizations of squeezed coherent states do not exist in the Hilbert space of the simple harmonic oscillator, L/sub 2/(SHO). This is accomplished by showing that the generalized squeeze operators exp(z/sub k/(a/sup dagger/)/sup k/+ih/sub k/-1-(z/sub k/)*a/sup k/) are unbounded in L/sub 2/(SHO) for all k>2, where h/sub k/-1 is a Hermitian polynomial in a and a/sup dagger/ up to powers of (k-1).

• Research Organization: Chemistry Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545
• OSTI ID: 6810511
• Journal Information: Phys. Rev. D; (United States), Vol. 29:6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
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POLYNOMIALS
QUANTUM MECHANICS
VACUUM STATES
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657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics