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Modern Physics Letters A

New method for merging several exponential operators’ product into one exponential operator

Chunzao Zhang, Hong-Yi Fan

Published Nov 22, 2023• 2 citations
Publisher

Abstract

For two operators [Formula: see text] and [Formula: see text] which obey [Formula: see text]we shall prove [Formula: see text]which means we want to merge two exponential operators’ product into one exponential operator. This kind of operator identity is useful for calculating the quantum entropy [Formula: see text] since [Formula: see text] when [Formula: see text] but [Formula: see text] thus the merging operator formula is demanded. In this way, several exponential operators’ product can also be merged. We shall employ the method of integration within normally ordered product (IWOP) to derive the merging operator identity.

DOI
10.1142/s0217732323501584

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For two operators [Formula: see text] and [Formula: see text] which obey [Formula: see text]we shall prove [Formula: see text]which means we want to merge two exponential operators’ product into one exponential operator. This kind of operator identity is useful for calculating the quantum entropy [Formula: see text] since [Formula: see text] when [Formula: see text] but [Formula: see text] thus the merging operator formula is demanded. In this way, several exponential operators’ product can also be merged. We shall employ the method of integration within normally ordered product (IWOP) to derive the merging operator identity.
By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.