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On the Generation of Operator Equivalents and the Calculation of Their Matrix Elements

โœ Scribed by I.D. Ryabov

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
64 KB
Volume
140
Category
Article
ISSN
1090-7807

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โœฆ Synopsis

To find all components T ุŽq (k) โ€ซุโ€ฌ N k,q J ุŽ q ยฅ mโ€ซ0ุโ€ฌ kุŠq (ุŽ1) kุŠm a(k, q; m)J z m (0 < q < k) of an irreducible tensor operator of rank k, a recursion formula for the coefficients a(k, q; m) is derived. Various kinds of operator equivalents and forms of their expression are examined. Matrix elements of operator equivalents are expressed through the coefficients a(k, q; m). A table for the coefficients a(k, q; m) with k โ€ซุโ€ฌ 2, 4, and 6 is given.

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## Abstract In this paper we consider Hankel operators $ \tilde H \_{{\bar z}^k}$ = (__Id__ โ€“ __P__ ~1~)$ \bar z^k $ from __A__ ^2^(โ„‚, |__z__ |^2^) to __A__ ^2,1^(โ„‚, |__z__ |^2^)^โŠฅ^. Here __A__ ^2^(โ„‚, |__z__ |^2^) denotes the Fock space __A__ ^2^(โ„‚, |__z__ |^2^) = {__f__: __f__ is entire and โ€–__f_