New Operator Ordering Formulas Related to Hermite Polynomials Derived by Virtue of IWOP Technique |
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Authors: | FAN Hong-Yi |
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Institution: | Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China; Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China |
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Abstract: | By virtue of the technique of integration
within an ordered product
of operators and the fundamental operator identity $H_n(X)=2^n:X^n:$,
where $X$ is the coordinate operator and $H_n$ is the $n$-order
Hermite polynomials, : : is the normal ordering symbol, we not only
simplify the derivation of the main properties of Hermite polynomials, but
also directly derive some new operator identities regarding to
$H_n(X)$. Operation for transforming $f(X)\rightarrow :f(X):$ is also
discussed. |
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Keywords: | IWOP technique Hermite polynomials |
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