Simplified algebraic description of weak measurements with Hermite–Gaussian and Laguerre–Gaussian pointer states

Weak measurements are recognized as a very powerful tool in measuring tiny effects that are perpendicular to the propagation direction of a light beam. In this paper, we develop a simple algebraic description of the weak measurement protocol for both Laguerre–Gaussian and Hermite–Gaussian pointer states in the Schrödinger representation. Since a novel class of position and momentum expectation values could be derived, the present scenario appeared to be very efficient and insightful when compared to analytical methods.