Expectation values and trace over the environment

[deneve]

I've worked through a Stern Gerlach experiment for the S_x and S_z directions using the density matrix formalism to account for the environment. This shows a result which I think is correct but relies on decoherence to give the "actual" value. I'm not confident about the result though. Would anyone be kind enough to check my reasoning and conclusions please? Working is attached.

 

[eljose79]

Dear fellow scientist,

Thank you for sharing your work on the Stern Gerlach experiment with us. I commend you for using the density matrix formalism to account for the environment, as it is a powerful tool in studying quantum systems.

I have reviewed your attached work and I must say that your reasoning and conclusions seem to be sound. Decoherence is indeed a crucial factor in obtaining the "actual" value in this experiment. It is important to take into account the interactions between the system and its environment, as they can lead to a loss of coherence and affect the measurement outcomes.

I would suggest that you also consider the time evolution of the density matrix in your analysis. This can provide further insights into the dynamics of the system and its interaction with the environment.

Overall, I believe your work is a valuable contribution to the understanding of the Stern Gerlach experiment and the role of decoherence in quantum measurements. Keep up the good work and I look forward to seeing more of your research in the future.