(a) Show that the action of the position operator in the momentum space is given by = ih Hint: Evaluate (pây) dp (b) Show that (pleFipo/h|v) = √(p±po). Thus, the position operator is the generator of translations in momentum space (c) If & and p are the position and momentum operators, and f(p) is a function of momentum variable p, [ƒ(p), â] = -iħd! (p) dp
(a) Show that the action of the position operator in the momentum space is given by = ih Hint: Evaluate (pây) dp (b) Show that (pleFipo/h|v) = √(p±po). Thus, the position operator is the generator of translations in momentum space (c) If & and p are the position and momentum operators, and f(p) is a function of momentum variable p, [ƒ(p), â] = -iħd! (p) dp
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![(a) Show that the action of the position operator in the momentum space is given
by â = ih Hint: Evaluate (pây)
(b) Show that
(p/eFipo/hy) = (p±po).
Thus, the position operator is the generator of translations in momentum
space
(c) Ifâ and p are the position and momentum operators, and f(p) is a function of
momentum variable p, [ƒ(p), â] =-iħd! (p)
dp](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8400ff80-3644-4e64-8dd8-3b136c5ec31f%2F2ce307c6-4b2a-44ad-ab06-718369ce3706%2F0215xzr_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Show that the action of the position operator in the momentum space is given
by â = ih Hint: Evaluate (pây)
(b) Show that
(p/eFipo/hy) = (p±po).
Thus, the position operator is the generator of translations in momentum
space
(c) Ifâ and p are the position and momentum operators, and f(p) is a function of
momentum variable p, [ƒ(p), â] =-iħd! (p)
dp
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