Professor M does Science | Even and odd operators in quantum mechanics @ProfessorMdoesScience | Uploaded March 2021 | Updated October 2024, 2 hours ago.
What are even and odd operators?

📚 Simply put, even operators commute with the parity operator, and odd operators anticommute with the parity operator. Of these, even operators are the most interesting and useful because they share a common set of eigenstates with the parity operator. This implies that the eigenstates of even operators are either even or odd states. There are many systems described by even Hamiltonians (from the infinite square well to the hydrogen atom), and in all these systems we can, before doing any calculations, say that the energy eigenstates must be even or odd states.

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⏮️ BACKGROUND
Parity operator: youtu.be/OsvXeTEQxyg
Compatible observables: youtu.be/IhJvX4H7xkA
Wave functions: youtu.be/2lr3aA4vaBs
Projection operators: youtu.be/M9V4hhqyrKQ
Eigenvalues and eigenstates: youtu.be/p1zg-c1nvwQ

⏭️ WHAT NEXT?
Infinite square well: youtu.be/pbZN8Pd8kac
Quantum harmonic oscillator: [COMING SOON]
Hydrogen atom: [COMING SOON]

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Director and writer: BM
Producer and designer: MC