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PureMathematics
n
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,2023,13(1),15-23
PublishedOnlineJanuary2023inHans.https://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2023.131002
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TheTimeOperatoroftheTruncation
OperatoroftheNumberOperatorActing
onBernoulliFunctional
TingYang,LixiaZhang
∗
,CaishiWang
†
CollegeofMathematicsandStatistics,NorthwestNormalUniversity,LanzhouGansu
Received:Dec.4
th
,2022;accepted:Jan.5
th
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th
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[J].
n
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DOI:10.12677/pm.2023.131002
x
Abstract
Inthispaper,usingthetimeoperatortheoryofself-adjointoperator,weconstructthe
timeofthetruncationoperatorofthenumberoperatoractingonBernoullifunctional
whichiscloselyrelatedtothequantumBernoullinoiseandprovethatthethetime
operatorisnotunique.
Keywords
Numb erOperator,TimeOperator,QuantumBernoulliNoise
Copyright
c
2023byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution International License (CCBY 4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/pm.2023.13100219
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DOI:10.12677/pm.2023.13100220
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1
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1
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) =
i
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p
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DOI:10.12677/pm.2023.13100221
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k
T
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n
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=
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n
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[1]Privault, N. (2008)Stochastic Analysis of Bernoulli Processes.
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[2]Wang,C.S.,Lu,Y.C.andChai,H.F.(2011)AnAlternativeApproachtoPrivault’sDiscrete-
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[8]Wang, C.S., Chai, H.F.andLu, Y.C. (2010)Discrete-Time QuantumBernoulli Noises.
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