Answer the following about operators in quantum mechanics, for 10 points each.
[10m] In the language of quantum mechanics, operators act on these representations of state vectors. The exterior product of one of these things with its dual gives a projection operator.
ANSWER: kets [reject “bra-ket” or “bra-ket notation”]
[10e] Quantum mechanical operators possess this property that means an operator acting on a sum of kets equals the sum of the operator acting on each ket. Functional analysis and a branch of algebra named for this property are the foundation for studying wave functions as vectors in Hilbert spaces.
ANSWER: linearity [accept linear algebra]
[10h] This result states that any Hermitian operator’s expectation value can be expressed as the integral of a real parameter lambda with respect to a projection-valued measure.
ANSWER: spectral theorem
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