What is the spectrum of an operator?

• The set of all state vectors
• The menu of results a measurement can return
• The list of all possible operators

Why are observables represented by Hermitian operators rather than by any matrix at all?

• Hermitian operators always have real eigenvalues
• Hermitian operators are always diagonal
• Any matrix has real eigenvalues

A Hermitian operator can have a non-real eigenvalue.

Circle one:   True   False

What do orthogonal eigenvectors mean physically?

• Outcomes always occur together
• The operator has no eigenvalues
• Distinct outcomes match distinct, non overlapping states

A state is expanded in an observable's eigenbasis with weights 0.6 and 0.8. What are the measurement probabilities?

• 0.6 and 0.8
• 0.36 and 0.64
• 0.3 and 0.4

What changes when an observable has a continuous spectrum, like position?

• Probabilities come from densities with a different normalization
• Eigenvalues stop being real
• Every outcome becomes equally likely

A state is 0.6 times one energy eigenstate plus 0.8 times another. What is the probability of measuring the second energy?

Answer: ______________

What do sharp spectral lines in an atomic spectrum record?

• Direct photographs of electron orbits
• Jumps between definite energies, marking eigenvalues indirectly
• Noise in the detector