What is a Hermitian operator?
Understand the Problem
The question is asking for the definition and properties of a Hermitian operator, which is a concept from linear algebra and quantum mechanics. This involves understanding how such operators behave and their significance in mathematical physics.
Answer
A linear operator that is equal to its own Hermitian adjoint.
A Hermitian operator is a linear operator that is equal to its own Hermitian adjoint (conjugate transpose).
Answer for screen readers
A Hermitian operator is a linear operator that is equal to its own Hermitian adjoint (conjugate transpose).
More Information
Hermitian operators have real eigenvalues and are often associated with observable physical quantities in quantum mechanics.
Tips
common mistakes include confusing Hermitian operators with symmetric operators, which are a special case in finite dimensions.
Sources
- 8.6.1: Hermitian Operators - Chemistry LibreTexts - chem.libretexts.org
- Hermitian Operator: Properties & Real Eigenvalues - Vaia - vaia.com
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