Even and odd operators in quantum mechanics
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: • The parity operator in quantum mechanics
Compatible observables: • Compatible observables in quantum mechanics
Wave functions: • Wave functions in quantum mechanics
Projection operators: • Projection operators in quantum mechanics
Eigenvalues and eigenstates: • Eigenvalues and eigenstates in quantum mec...
⏭️ WHAT NEXT?
Infinite square well: • Infinite square well in quantum mechanics
Quantum harmonic oscillator: [COMING SOON]
Hydrogen atom: [COMING SOON]
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