Show that the radial wave function takes the form R n ( n − 1 ) = N n r n − 1 e − r / n a , when l = n − 1 using the recursion formula and determine the normalization constant N n by direct integration.

Question

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Answer 1

Question

Chapter 4, Problem 4.55P

(a)

To determine

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

(b)

To determine

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

(c)

To determine

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

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Answer 2

Question

Chapter 4, Problem 4.55P

(a)

To determine

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

(b)

To determine

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

(c)

To determine

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 4, Problem 4.55P

(a)

To determine

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

(b)

To determine

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

(c)

To determine

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 4, Problem 4.55P

(a)

To determine

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

(b)

To determine

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

(c)

To determine

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

Expert Solution & Answer

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Answer 5

Chapter 4, Problem 4.55P

(a)

To determine

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

(b)

To determine

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

(c)

To determine

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

Answer 6

Chapter 4, Problem 4.55P

(a)

To determine

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

Answer 7

Chapter 4, Problem 4.55P

(a)

To determine

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

Answer 8

(b)

To determine

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

Answer 9

(b)

To determine

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

Answer 10

(c)

To determine

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

Answer 11

(c)

To determine

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 4.1 - Prob. 4.1P Ch. 4.1 - Prob. 4.3P Ch. 4.1 - Prob. 4.4P Ch. 4.1 - Prob. 4.5P Ch. 4.1 - Prob. 4.6P Ch. 4.1 - Prob. 4.7P Ch. 4.1 - Prob. 4.8P Ch. 4.1 - Prob. 4.9P Ch. 4.1 - Prob. 4.10P Ch. 4.1 - Prob. 4.11P

Show that the radial wave function takes the form R n ( n − 1 ) = N n r n − 1 e − r / n a , when l = n − 1 using the recursion formula and determine the normalization constant N n by direct integration.

Show that the radial wave function takes the form Rn(n−1)=Nnrn−1e−r/na, when l=n−1 using the recursion formula and determine the normalization constant Nn by direct integration.

The expectation value of 〈r〉 and 〈r2〉 for states of the form ψn(n−1)m.

Show that the “uncertainty” in r(σr) is 〈r〉/2n+1 for such states. Also sketch the radial wave functions for several values of n.

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Chapter 4 Solutions