I Commutation of Beam splitter operator with Displacement operator

deepalakshmi
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Does Beam splitter operator and Displacement operator of coherent state commute with each other?
I have a beam splitter operator (a†)b +(b†)a. Does it commute with exp(αâ†-α*â). Here a and ↠are creation and lowering operator
 
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Well, just check, whether the BS operator commutes with the argument of the operator exponential!
 

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