Schrodinger's Equation & Measurement

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SUMMARY

This discussion centers on the implications of performing measurements in quantum mechanics, specifically in relation to Schrodinger's Equation. It establishes that measurements taken before a predicted time, such as time8, can alter the original probability predictions derived from time0. The conversation highlights the necessity of incorporating measurement data into the unitary operator to adjust these probabilities, emphasizing the flexibility of the wave equation in accommodating time variations or simplifications.

PREREQUISITES
  • Understanding of Schrodinger's Equation
  • Familiarity with quantum mechanics concepts such as wave functions and probability amplitudes
  • Knowledge of unitary operators in quantum theory
  • Basic grasp of measurement theory in quantum mechanics
NEXT STEPS
  • Explore the role of measurements in quantum mechanics and their effects on wave functions
  • Study the mathematical formulation of unitary operators in quantum systems
  • Investigate the implications of time-dependent versus time-independent Schrodinger's Equation
  • Learn about the concept of quantum state collapse and its relation to measurements
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Quantum physicists, students of quantum mechanics, and researchers interested in the foundational aspects of measurement theory and its impact on quantum predictions.

StevieTNZ
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Hi there,

Ok, so if you know the interactions, etc., you can calculate from time0 the probabilities for certain results at say time8.

But say, however, we perform a measurement before time8. Will the original predictions for time8 still hold if a measurement is performed prior to that time? Or will it be different - in that case, what information do you need from the measurement, to plug into the unitary operator (which will include interactions, etc.) to find the new probabilities at time8?
 
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StevieTNZ said:
Hi there,

Ok, so if you know the interactions, etc., you can calculate from time0 the probabilities for certain results at say time8.

But say, however, we perform a measurement before time8. Will the original predictions for time8 still hold if a measurement is performed prior to that time? Or will it be different - in that case, what information do you need from the measurement, to plug into the unitary operator (which will include interactions, etc.) to find the new probabilities at time8?

The wave equation can be set up to be as complicated or simple as you like. It is possible to include variation of the equation over time, or make the simplifying assumption that nothing varies over time. It is up to you.
 

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