Use the commutator results, [â, ô] = iħ, [x²,p] = 2iħâ, and [ÂÂ, Ĉ] = Â[Â, Ĉ] + [Â‚ Ĉ]B,to find the commutators given below.(a) [x, p²](b) [x³, p](c) [x², p²]

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Answered: Use the commutator results, [ŵ, ô] =…

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Use the commutator results, [â, ô] = iħ, [x²,p] = 2iħâ, and [ÂÂ, Ĉ] = Â[Â, Ĉ] + [Â‚ Ĉ]B,
to find the commutators given below.
(a) [x, p²]
(b) [x³, p]
(c) [x², p²]

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$G i v e n comma open square brackets x with hat on top comma space p with hat on top close square brackets space equals space i ħ open square brackets x with hat on top squared comma space p with hat on top close square brackets space equals 2 space i ħ x with hat on top G e n e r a l space f o r m u l a colon open square brackets A with hat on top comma space B with hat on top to the power of n close square brackets space equals n B with hat on top to the power of n minus 1 end exponent open square brackets A with hat on top comma space B with hat on top close square brackets open square brackets A with hat on top to the power of n comma space B with hat on top close square brackets space equals n A with hat on top to the power of n minus 1 end exponent open square brackets A with hat on top comma space B with hat on top close square brackets left parenthesis a right parenthesis open square brackets space x with hat on top comma space p with hat on top squared close square brackets space equals space 2 space p with hat on top to the power of left parenthesis 2 minus 1 right parenthesis end exponent open square brackets x with hat on top comma space p with hat on top close square brackets space equals 2 space p with hat on top open square brackets x with hat on top comma space p with hat on top close square brackets space box enclose 2 space p with hat on top open square brackets x with hat on top comma space p with hat on top close square brackets equals 2 space p with hat on top space i ħ end enclose left parenthesis b right parenthesis space open square brackets x with hat on top cubed comma space p with hat on top close square brackets space equals space 3 space x with hat on top to the power of left parenthesis 3 minus 1 right parenthesis end exponent open square brackets x with hat on top comma space p with hat on top close square brackets space equals 3 space x with hat on top squared space i ħ box enclose open square brackets x with hat on top cubed comma space p with hat on top close square brackets equals 3 space x with hat on top squared space i ħ end enclose$

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Use the commutator results, [ŵ, ô] = iħ, [x²,p] = 2iħâ, and [ÂÂ, Ĉ] = Â[B, Ĉ] + [Â‚Ĉ]Â, to find the commutators given below. (a) [x, p²] (b) [x³,p] (c) [x², p²]