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https://texercises.com/exercise/variance/
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Exercise:
The variance of an observable A is defined as sigma^ langle leftA - langle A rangleright^ rangle Show that the variance corresponds to sigma^ langle A^ rangllangle A rangle^

Solution:
sigma^ langla leftA-langle A rangleright^rangle langle A^-Alangle A rangle + langle A rangle^ rangle langle A^ rangle - langle Alangle A ranglerangle + langle langle A rangle^ rangle Since the expectation value is a real number and the expectation value of a number is just that number this can be simplified as sigma^ langle A^rangle -langle A ranglelangle A rangle + langle A rangle^ langle A^ rangle - langle A rangle^
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Exercise:
The variance of an observable A is defined as sigma^ langle leftA - langle A rangleright^ rangle Show that the variance corresponds to sigma^ langle A^ rangllangle A rangle^

Solution:
sigma^ langla leftA-langle A rangleright^rangle langle A^-Alangle A rangle + langle A rangle^ rangle langle A^ rangle - langle Alangle A ranglerangle + langle langle A rangle^ rangle Since the expectation value is a real number and the expectation value of a number is just that number this can be simplified as sigma^ langle A^rangle -langle A ranglelangle A rangle + langle A rangle^ langle A^ rangle - langle A rangle^
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quantum physics
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expectation value, probability, variance
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ENG (English)
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Calculative / Quantity
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