Concept explainers
(a)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In
Answer to Problem 11.22E
The given integral is identically zero.
Explanation of Solution
The wavefunction
The wavefunction
Substitute the value of
The integration of harmonic oscillator is solved using Hermite polynomials. The integral of Hermite polynomials is solved by the formula given in Table 11.2.
In the given integral, the wavefunctions are
The given integral is identically zero.
(b)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.22E
The given integral is identically zero.
Explanation of Solution
The wavefunction
Substitute the value of
In the above equation,
The given integral is identically zero.
(c)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.22E
The given integral is not identically zero.
Explanation of Solution
The wavefunction
Substitute the value of
In the above equation,
The given integral is not identically zero.
(d)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.22E
The given integral is identically zero.
Explanation of Solution
The wavefunction
The wavefunction
Substitute the value of
The integration of harmonic oscillator is solved using Hermite polynomials. The integral of Hermite polynomials is solved by the formula given in Table 11.2.
In the given integral, the wavefunctions are
The given integral is identically zero.
(e)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.22E
The given integral is not identically zero.
Explanation of Solution
The wavefunction
Substitute the value of
The integration of harmonic oscillator is solved using Hermite polynomials. The integral of Hermite polynomials is solved by the formula given in Table 11.2.
In the given integral, the wavefunctions are
The given integral is not identically zero.
(f)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 11.22E
The given integral is indeterminate.
Explanation of Solution
The wavefunction
Substitute the value of
In the above equation,
The given integral is indeterminate.
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Chapter 11 Solutions
Physical Chemistry
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