(a) Interpretation: The approximate energies of the real system are to be evaluated if H 12 = H 21 = − 0.50 (arbitrary energy units). Concept introduction: The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

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Answer 1

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

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At what radius does the probability density of an electron in the H atom fall to 50 per cent of its maximum value?

Answer 2

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Expert Solution & Answer

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Answer 3

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Expert Solution & Answer

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Answer 4

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Expert Solution & Answer

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Answer 5

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Answer 6

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Answer 7

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Answer 10

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Answer 11

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Answer 12

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Answer 13

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Solution Summary: The author explains that the secular determinant is used to solve the linear variation theory.

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