Expectation values and trace over the environment

In summary: Your Name]In summary, the conversation discusses the use of the density matrix formalism in the Stern Gerlach experiment to account for the environment and the importance of decoherence in obtaining the "actual" value. The speaker has reviewed the attached work and finds the reasoning and conclusions to be sound, suggesting the consideration of the time evolution of the density matrix for further insights. The work is seen as a valuable contribution to understanding the experiment and the role of decoherence.
  • #1
deneve
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I've worked through a Stern Gerlach experiment for the Sx and Sz 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.
 

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  • Expectation values for paper-1.pdf
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  • #2


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.
 

1. What is the concept of expectation values in physics?

Expectation values, also known as average values, are a way to calculate the average result of a measurement in quantum mechanics. It represents the most likely outcome of a measurement when repeated multiple times.

2. How are expectation values calculated?

To calculate the expectation value of a physical quantity, we multiply the possible outcomes of the measurement by their probabilities and then add them together. This is represented mathematically as the integral of the product of the observable and the probability density function.

3. How does trace over the environment work in quantum mechanics?

Trace over the environment is a mathematical operation used to calculate the reduced density matrix of a quantum system. It involves summing over all possible states of the environment to obtain the probability of a given state of the system. This allows us to study the behavior of the system without taking into account the details of the environment.

4. What is the significance of expectation values in quantum mechanics?

Expectation values play a crucial role in quantum mechanics as they represent the most probable outcome of a measurement. They also provide a way to compare theoretical predictions with experimental results, making them an important tool in understanding the behavior of quantum systems.

5. Can expectation values be measured experimentally?

Yes, expectation values can be measured experimentally. In quantum mechanics, the expectation value of a physical quantity is the average result of a measurement when repeated multiple times. By performing experiments multiple times and taking the average, we can determine the expectation value of a specific physical quantity.

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