4. Calculate the following commutators (Recall that [Â, B] = ÂB – BÂ= -[B, Â]) (a) [&, 최 (b) [â, p] (c) [â², p]

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4. Calculate the following commutators
(Recall that [Â, B] = ÂB – BÂ= -[B, Â)
(a) [â, î]
(b) [â, î]
(c) [â²,p]
(d) [â, ƒ(â)]
(e) [p, f(â)]
(f) [î, H] for general potential V (x)
Transcribed Image Text:4. Calculate the following commutators (Recall that [Â, B] = ÂB – BÂ= -[B, Â) (a) [â, î] (b) [â, î] (c) [â²,p] (d) [â, ƒ(â)] (e) [p, f(â)] (f) [î, H] for general potential V (x)
Expert Solution
Step 1

a)

Given,

commutator is,

x^,x^

solving this,

x^,x^=x^x^-x^x^

Since position operator is written as x^=x

Then

x^,x^=xx-xx=0

so commutation relation of x^,x^ is 0

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