Bi-coherent states as generalized eigenstates of the position and the momentum operators
Bi-coherent states as generalized eigenstates of the position and the momentum operators
Abstract In this paper, we show that the position and the derivative operators, $${{\hat{q}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> and $${{\hat{D}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> , can be treated as ladder operators connecting various vectors of two biorthonormal families, $${{{\mathcal {F}}}}_\varphi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> …