Uncertainty Principle
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Introduction
Introduction
1. Introduction to Heisenberg Uncertainty
An educational presentation on Heisenberg's Uncertainty Principle, exploring its formal statement, operator origins, and physical meaning for advanced students.
Foundations
Foundations
2. What Uncertainty Means in QM
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Foundations
3. Wavefunction and Probability
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Foundations
4. Momentum as a Differential Operator
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Fundamentals
Fundamentals
5. Non-Commuting Operators
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Fundamentals
6. General Uncertainty Theorem
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Derivations
Derivations
7. Derivation Overview
Using Cauchy–Schwarz inequality on centered operators \( \Delta\hat{A}, \Delta\hat{B} \), derive Robertson bound. Explain decomposition of inner product into commutator and anticommutator.
Special Cases
Special Cases
8. Specialization to Position and Momentum
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Special Cases
9. Minimum-Uncertainty States
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Conclusion
Conclusion
10. Summary and Takeaways
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Uncertainty Principle