The proof for the commutator identities [ A ^ + B ^ , C ^ ] = [ A ^ , C ^ ] + [ B ^ , C ^ ] and [ A ^ B ^ , C ^ ] = A ^ [ B ^ , C ^ ] + [ A ^ , C ^ ] B ^

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Answer 1

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Chapter 3.5, Problem 3.14P

(a)

To determine

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

(b)

To determine

The prove that [xn,p^]=iℏbxn−1.

(c)

To determine

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

(d)

To determine

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

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Prove that F= m (2x/t^2) from equations (2.1) – (2.4).

Answer 2

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Chapter 3.5, Problem 3.14P

(a)

To determine

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

(b)

To determine

The prove that [xn,p^]=iℏbxn−1.

(c)

To determine

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

(d)

To determine

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

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See solution

Answer 3

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Chapter 3.5, Problem 3.14P

(a)

To determine

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

(b)

To determine

The prove that [xn,p^]=iℏbxn−1.

(c)

To determine

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

(d)

To determine

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

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Answer 4

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Chapter 3.5, Problem 3.14P

(a)

To determine

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

(b)

To determine

The prove that [xn,p^]=iℏbxn−1.

(c)

To determine

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

(d)

To determine

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

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Answer 5

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Answer 6

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Answer 7

Chapter 3.5, Problem 3.14P

(a)

To determine

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

(b)

To determine

The prove that [xn,p^]=iℏbxn−1.

(c)

To determine

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

(d)

To determine

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

Answer 8

Chapter 3.5, Problem 3.14P

(a)

To determine

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

Answer 9

Chapter 3.5, Problem 3.14P

(a)

To determine

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

Answer 10

(b)

To determine

The prove that [xn,p^]=iℏbxn−1.

Answer 11

(b)

To determine

The prove that [xn,p^]=iℏbxn−1.

Answer 12

(c)

To determine

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

Answer 13

(c)

To determine

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

Answer 14

(d)

To determine

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

Answer 15

(d)

To determine

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 3.1 - Prob. 3.1P Ch. 3.1 - Prob. 3.2P Ch. 3.2 - Prob. 3.3P Ch. 3.2 - Prob. 3.4P Ch. 3.2 - Prob. 3.5P Ch. 3.2 - Prob. 3.6P Ch. 3.3 - Prob. 3.7P Ch. 3.3 - Prob. 3.8P Ch. 3.3 - Prob. 3.9P Ch. 3.3 - Prob. 3.10P

The proof for the commutator identities [ A ^ + B ^ , C ^ ] = [ A ^ , C ^ ] + [ B ^ , C ^ ] and [ A ^ B ^ , C ^ ] = A ^ [ B ^ , C ^ ] + [ A ^ , C ^ ] B ^

The proof for the commutator identities [A^+B^,C^]=[A^,C^]+[B^,C^] and [A^B^,C^]=A^[B^,C^]+[A^,C^]B^

The prove that [xn,p^]=iℏbxn−1.

The proof that [f(x),p^]=iℏdfdx for any function f(x) that admits a Taylor series expansion.

The proof [H^,a^±]=±ℏωa^± for simple harmonic oscillator.

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Chapter 3 Solutions