Physics · University
Quantum states, amplitudes and measurement · revision notes
A normalized state vector encodes probability amplitudes. Overall global phase leaves measurement probabilities unchanged.
Key ideas and conditions
States
A normalized state vector encodes probability amplitudes. Overall global phase leaves measurement probabilities unchanged.
Born rule
For an orthonormal measurement basis, outcome probability is the squared magnitude of the corresponding amplitude, not the amplitude itself.
Expectation
An observable expectation is the probability-weighted mean of its possible outcomes. A single measurement need not equal that mean.
Learning scope
These finite-dimensional examples introduce quantum reasoning. They are not a complete treatment of Hilbert spaces or laboratory control.
Explain without looking
- For amplitudes i/√2 and 1/√2, what are the probabilities?
- What information is missing if only outcome probabilities in one basis are supplied?
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
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