On von Neumann's hypothesis of collapse of the wave function and quantum Zeno paradox in continuous measurement

Abstract

The experiment performed by Itano, Heinzen, Bollinger and Wineland on the quantum Zeno effect is analyzed in detail through a quantum map derived by conventional quantum mechanics based on the Schrodinger equation. The analysis shows that a slight modification of their experiment leads to a significantly different result from the one that is predicted through von Neumann's hypothesis of collapse of the wave function in the quantum measurement theory. This may offer a possibility of an experimental test of von Neumann's quantum measurement theory.