The time reversal of the operators x ^ ′ , p ^ ′ .

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Answer 1

Question

Chapter 6, Problem 6.36P

(a)

To determine

The time reversal of the operators x^′,p^′.

(b)

To determine

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

(c)

To determine

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

(d)

To determine

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

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Consider the situation in the figure below; a neutral conducting ball hangs from the ceiling by an insulating string, and a charged insulating rod is going to be placed nearby. A. First, if the rod was not there, what statement best describes the charge distribution of the ball? 1) Since it is a conductor, all the charges are on the outside of the ball. 2) The ball is neutral, so it has no positive or negative charges anywhere. 3) The positive and negative charges are separated from each other, but we don't know what direction the ball is polarized. 4) The positive and negative charges are evenly distributed everywhere in the ball. B. Now, when the rod is moved close to the ball, what happens to the charges on the ball? 1) There is a separation of charges in the ball; the side closer to the rod becomes positively charged, and the opposite side becomes negatively charged. 2) Negative charge is drawn from the ground (via the string), so the ball acquires a net negative charge. 3)…

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Answer 2

Question

Chapter 6, Problem 6.36P

(a)

To determine

The time reversal of the operators x^′,p^′.

(b)

To determine

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

(c)

To determine

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

(d)

To determine

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

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Answer 3

Question

Chapter 6, Problem 6.36P

(a)

To determine

The time reversal of the operators x^′,p^′.

(b)

To determine

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

(c)

To determine

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

(d)

To determine

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

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Answer 4

Question

Chapter 6, Problem 6.36P

(a)

To determine

The time reversal of the operators x^′,p^′.

(b)

To determine

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

(c)

To determine

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

(d)

To determine

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

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Answer 5

Chapter 6, Problem 6.36P

(a)

To determine

The time reversal of the operators x^′,p^′.

(b)

To determine

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

(c)

To determine

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

(d)

To determine

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

Answer 6

Chapter 6, Problem 6.36P

(a)

To determine

The time reversal of the operators x^′,p^′.

Answer 7

Chapter 6, Problem 6.36P

(a)

To determine

The time reversal of the operators x^′,p^′.

Answer 8

(b)

To determine

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

Answer 9

(b)

To determine

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

Answer 10

(c)

To determine

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

Answer 11

(c)

To determine

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

Answer 12

(d)

To determine

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

Answer 13

(d)

To determine

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 6.1 - Prob. 6.1P Ch. 6.2 - Prob. 6.2P Ch. 6.2 - Prob. 6.3P Ch. 6.2 - Prob. 6.4P Ch. 6.2 - Prob. 6.5P Ch. 6.2 - Prob. 6.7P Ch. 6.4 - Prob. 6.8P Ch. 6.4 - Prob. 6.9P Ch. 6.4 - Prob. 6.10P Ch. 6.4 - Prob. 6.11P

The time reversal of the operators x ^ ′ , p ^ ′ .

Solution Summary: The author explains the time reversal of the operators stackrelxprime, and the arbitrary function.

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The time reversal of the operators x^′,p^′.

The proof that time reversal invariance requires commutation of the time reversal operator with Hamiltonian operator.

The proof that for a time reversal invariant Hamiltonian, the complex conjugate of the stationary state wavefunction also has the same eigen value.

The time reversal for a momentum eigen function, for hydrogen wave function. Also, the verification of part (c).

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Chapter 6 Solutions