Theorem About Completeness of Quantum Mechanical Motion Group

Waniewski, J.

doi:10.1016/0034-4877(77)90073-8

Theorem About Completeness of Quantum Mechanical Motion Group

J. Waniewski
(
- Warsaw U.
)

1977

7 pages

Published in:

Rept.Math.Phys. 11 (1977) 331-337

DOI:

10.1016/0034-4877(77)90073-8

View in:

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Abstract: (Elsevier)

The imaginary Hamiltonians iH of the Schrödinger quantum mechanics generate a certain Lie algebra which is shown to contain the algebra of all skew-symmetric polynomials in the momentum and the position operators. The skew-adjoint closures of these polynomials, in turn, are shown to be dense in the strong resolvent sense in the set of all skew-adjoint operators. As a consequence, the smallest strong closure group containing all evolution operators for the Shrödinger particle is the whole unitary group.

QUANTUM MECHANICS: NONRELATIVISTIC
QUANTUM MECHANICS: OPERATOR ALGEBRA
ALGEBRA: LIE
GROUP THEORY
FUNCTIONAL ANALYSIS: linear space

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Figures(0)

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