A　simple　and　neat　approach　to　derive　the　recurrence　relations　and mathematical　integral　formulas　of　two-variable　Hermite　polynomial

LI　Heng-mei1; WAN　Zhi-long1; WANG　Zhen1; HUANG　Hong-yun1; YUAN　Hong-chun2

doi:10.16854/j.cnki.1000-0712.2017.12.004

2017 , Vol. 36 >Issue 12: 15 - 17

DOI: https://doi.org/10.16854/j.cnki.1000-0712.2017.12.004

A　simple　and　neat　approach　to　derive　the　recurrence　relations　and mathematical　integral　formulas　of　two-variable　Hermite　polynomial

LI　Heng-mei1 ,
WAN　Zhi-long1 ,
WANG　Zhen1 ,
HUANG　Hong-yun1 ,
YUAN　Hong-chun2

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1.College　of　Mathematical　Physics　and　Chemical　Engineering，Changzhou　Institute　of　Technology，Changzhou，Jiangsu　213022，China; 2.College　of　Electrical　and　Optoelectronic　Engineering，Changzhou　Institute　of　Technology，Changzhou，Jiangsu　213022，China

Received date: 2017-05-27

Revised date: 2017-07-20

Online published: 2017-12-20

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Abstract

Based　on　the　properties　of　normal(anti-normal)ordering　product　of　quantum　operators　and Baker-Hausdorff　operator　equation，using　the　Gauss　integral　form　of　coherent　state　representation　completeness，we derive　some　operator　identities，recursive　relations　and　integral　formulas　related　to　two-variable　Hermite　polynomial.Compared　with　other　methods，this　method　is　easier　and　neater　in　theory　and　application.

Key words： two-variable　Hermite　polynomial; normal　ordering　product; anti-normal　ordering　product; recursive　relation; integral　formula

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LI　Heng-mei1 , WAN　Zhi-long1 , WANG　Zhen1 , HUANG　Hong-yun1 , YUAN　Hong-chun2 . A　simple　and　neat　approach　to　derive　the　recurrence　relations　and mathematical　integral　formulas　of　two-variable　Hermite　polynomial[J]. College Physics, 2017 , 36(12) : 15 -17 . DOI: 10.16854/j.cnki.1000-0712.2017.12.004

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