Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

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Answer 1

Question

Chapter 8, Problem 8.29P

(a)

To determine

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

(b)

To determine

Verify the corollary that every potential well in one-dimension posses a bound state.

(c)

To determine

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

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Answer 2

Question

Chapter 8, Problem 8.29P

(a)

To determine

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

(b)

To determine

Verify the corollary that every potential well in one-dimension posses a bound state.

(c)

To determine

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

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Answer 3

Question

Chapter 8, Problem 8.29P

(a)

To determine

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

(b)

To determine

Verify the corollary that every potential well in one-dimension posses a bound state.

(c)

To determine

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

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Answer 4

Question

Chapter 8, Problem 8.29P

(a)

To determine

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

(b)

To determine

Verify the corollary that every potential well in one-dimension posses a bound state.

(c)

To determine

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

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Answer 5

Chapter 8, Problem 8.29P

(a)

To determine

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

(b)

To determine

Verify the corollary that every potential well in one-dimension posses a bound state.

(c)

To determine

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

Answer 6

Chapter 8, Problem 8.29P

(a)

To determine

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

Answer 7

Chapter 8, Problem 8.29P

(a)

To determine

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

Answer 8

(b)

To determine

Verify the corollary that every potential well in one-dimension posses a bound state.

Answer 9

(b)

To determine

Verify the corollary that every potential well in one-dimension posses a bound state.

Answer 10

(c)

To determine

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

Answer 11

(c)

To determine

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 8.1 - Prob. 8.1P Ch. 8.1 - Prob. 8.2P Ch. 8.1 - Prob. 8.3P Ch. 8.1 - Prob. 8.4P Ch. 8.1 - Prob. 8.5P Ch. 8.1 - Prob. 8.6P Ch. 8.2 - Prob. 8.7P Ch. 8.2 - Prob. 8.8P Ch. 8.3 - Prob. 8.9P Ch. 8.3 - Prob. 8.10P

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

Solution Summary: The author demonstrates that if a potential well consists of one bound state, any deeper or wider well also possesses minimum one-bound state.

Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.

Verify the corollary that every potential well in one-dimension posses a bound state.

Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.

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Chapter 8 Solutions