Professor M does Science | Hermitian operators in quantum mechanics @ProfessorMdoesScience | Uploaded July 2020 | Updated October 2024, 3 hours ago.
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📚 Hermitian operators represent physical quantities in quantum mechanics. We first show that their eigenvalues, which give the possible outcomes of the measurement of a physical quantity, are always real numbers. Second, we show that their eigenstates, which tell us about the probability of obtaining a particular outcome for a measurement, form a basis of state space, so they can be used to represent any physical state.

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⏮️ BACKGROUND
Dirac notation in state space: youtu.be/hJoWM9jf0gU
Operators: youtu.be/pNFna7zZbgE
Representations: youtu.be/rp2k2oR5ZQ8
Matrix formulation: youtu.be/wIwnb1ldYTI
Eigenvalues and eigenstates: youtu.be/p1zg-c1nvwQ

⏭️ WHAT NEXT?
Compatible observables: youtu.be/IhJvX4H7xkA
Measurements | Concepts: youtu.be/u1R3kRWh1ek
Measurements | Maths: youtu.be/odLwUXKY0Js

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Director and writer: BM
Producer and designer: MC