Observable and interaction

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SUMMARY

The discussion centers on the Stern-Gerlach experiment, which demonstrates how an inhomogeneous magnetic field can separate particles based on their spin, thereby facilitating the measurement of quantum observables. The interaction energy, observable measurement, and interaction time are crucial components in this process. Participants seek to understand the relationship between these elements and whether general rules govern the observation of an observable, particularly in relation to its representation in the Hamiltonian of the system.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Stern-Gerlach experiment
  • Knowledge of Hamiltonian mechanics
  • Concept of quantum observables
NEXT STEPS
  • Research the mathematical formulation of the Stern-Gerlach experiment
  • Explore the role of Hamiltonians in quantum mechanics
  • Study the concept of quantum measurement theory
  • Investigate the relationship between interaction time and observable outcomes in quantum systems
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Physicists, quantum mechanics students, and researchers interested in the principles of quantum measurement and the implications of the Stern-Gerlach experiment.

lalbatros
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Let us consider the http://en.wikipedia.org/wiki/Stern-Gerlach_experiment" experiment.

The inhomogenuous magnetic field produces a drift force that can separate particles according to their spin and offer a possibility for a "measurement". This (very) small magnetic interaction can be embedded in the Hamiltonian of the system as an interaction. If this interaction is active during enough time the separation and also the "measurement" of the spin "observable" are made possible.

This famous experiment illustrates a link between:
an interaction energy
an observable (a "measurement")
a interaction time​

I would be interrested to know more about this link.

Thanks.

Michel
 
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In other words: how can an observable be "observed".
Are there general rules, or is it enough that this observable in some way appears in the Hamiltonian ? (With some sensibility?)

Michel
 

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