
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
- Calculate the pH and the pOH of each of the following solutions at 25 °C for which the substances ionize completely: (a) 0.000259 M HClO4arrow_forwardWhat is the pH of a 1.0 L buffer made with 0.300 mol of HF (Ka = 6.8 × 10⁻⁴) and 0.200 mol of NaF to which 0.160 mol of NaOH were added?arrow_forwardDetermine if the following salt is neutral, acidic or basic. If acidic or basic, write the appropriate equilibrium equation for the acid or base that exists when the salt is dissolved in aqueous solution. If neutral, simply write only NR. Be sure to include the proper phases for all species within the reaction. NaN₃arrow_forward
- A. Draw the structure of each of the following alcohols. Then draw and name the product you would expect to produce by the oxidation of each. a. 4-Methyl-2-heptanol b. 3,4-Dimethyl-1-pentanol c. 4-Ethyl-2-heptanol d. 5,7-Dichloro-3-heptanolarrow_forwardWhat is the pH of a 1.0 L buffer made with 0.300 mol of HF (Ka = 6.8 × 10⁻⁴) and 0.200 mol of NaF to which 0.160 mol of NaOH were added?arrow_forwardCan I please get help with this.arrow_forward
- Determine if the following salt is neutral, acidic or basic. If acidic or basic, write the appropriate equilibrium equation for the acid or base that exists when the salt is dissolved in aqueous solution. If neutral, simply write only NR. Be sure to include the proper phases for all species within the reaction. N₂H₅ClO₄arrow_forwardPlease help me with identifying these.arrow_forwardCan I please get help with this?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage Learning


