Abstract:

Quantum states together with operators provide the statistical description of any property of the system，which play important role in quantum theory. Based on coordinate and momentum quantum representations，a new kind of asymmetric integral projection operators is introduced，which is proved to be the Hermitian operator. By means of the technique of integration within an ordered product of operators，we obtain the normal ordering form of such Hermitian operator. In addition，it has been proved that such Herimtian operator corresponds to the parity measurement of the phase estimation in a MachZehnder interferometer .

Key words: quantum mechanics representation, Dirac symbol, projection operators, parity measurement