What the anti-symmetry under 1 ↔ 2 tells about the coefficients and invoke anti-symmetry under 2 ↔ 3 .

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Answer 1

Question

Chapter 5.1, Problem 5.10P

(a)

To determine

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

(b)

To determine

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

(c)

To determine

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

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Answer 2

Question

Chapter 5.1, Problem 5.10P

(a)

To determine

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

(b)

To determine

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

(c)

To determine

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

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Answer 3

Question

Chapter 5.1, Problem 5.10P

(a)

To determine

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

(b)

To determine

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

(c)

To determine

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

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Answer 4

Question

Chapter 5.1, Problem 5.10P

(a)

To determine

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

(b)

To determine

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

(c)

To determine

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

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Answer 5

Chapter 5.1, Problem 5.10P

(a)

To determine

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

(b)

To determine

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

(c)

To determine

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

Answer 6

Chapter 5.1, Problem 5.10P

(a)

To determine

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

Answer 7

Chapter 5.1, Problem 5.10P

(a)

To determine

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

Answer 8

(b)

To determine

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

Answer 9

(b)

To determine

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

Answer 10

(c)

To determine

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

Answer 11

(c)

To determine

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 5.1 - Prob. 5.1P Ch. 5.1 - Prob. 5.2P Ch. 5.1 - Prob. 5.3P Ch. 5.1 - Prob. 5.4P Ch. 5.1 - Prob. 5.5P Ch. 5.1 - Prob. 5.6P Ch. 5.1 - Prob. 5.8P Ch. 5.1 - Prob. 5.9P Ch. 5.1 - Prob. 5.10P Ch. 5.1 - Prob. 5.11P

What the anti-symmetry under 1 ↔ 2 tells about the coefficients and invoke anti-symmetry under 2 ↔ 3 .

Solution Summary: The author explains how the anti-symmetry under 1leftrightarrow 2 tells all the 8 coefficients are zero.

What the anti-symmetry under 1↔2 tells about the coefficients and invoke anti-symmetry under 2↔3.

The ground state, its energy and its degeneracy of the system with three identical non-interacting spin 12 particles in the infinite square well.

Show that the result from part (b) can be written in th e form Φ(1,2,3)=13[Φ(1,2)ϕ(3)−Φ(1,3)ϕ(2)+Φ(2,3)ϕ(1)].

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Chapter 5 Solutions