(a) Prove the following commutator identities: [à+ 8.ċ] = [Â.¿] + [â¸ċ]. (3.64) (3.65) (b) Show that [r", p] = i hnx"-!. (c) Show more generally that df (3.66) [Sx), p] = ih dx for any function f (x) that admits a Taylor series expansion. (d) Show that for the simple harmonic oscillator (3.67)
(a) Prove the following commutator identities: [à+ 8.ċ] = [Â.¿] + [â¸ċ]. (3.64) (3.65) (b) Show that [r", p] = i hnx"-!. (c) Show more generally that df (3.66) [Sx), p] = ih dx for any function f (x) that admits a Taylor series expansion. (d) Show that for the simple harmonic oscillator (3.67)
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![(a) Prove the following commutator identities:
[à+ 8.ċ] = [Â.¿] + [â¸ċ].
(3.64)
(3.65)
(b) Show that
[r", p] = i hnx"-!.
(c) Show more generally that
df
(3.66)
[Sx), p] = ih
dx
for any function f (x) that admits a Taylor series expansion.
(d) Show that for the simple harmonic oscillator
(3.67)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a4c5c7f-120e-4cd5-a2cd-d2b8263ea035%2Ffeff4600-21e5-4d9a-bbcf-b226d06f0187%2Ffi7d7h_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Prove the following commutator identities:
[à+ 8.ċ] = [Â.¿] + [â¸ċ].
(3.64)
(3.65)
(b) Show that
[r", p] = i hnx"-!.
(c) Show more generally that
df
(3.66)
[Sx), p] = ih
dx
for any function f (x) that admits a Taylor series expansion.
(d) Show that for the simple harmonic oscillator
(3.67)
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