Question

We shall see in Chapter 13 that the intensities of spectroscopic transitions between the vibrational states of a molecule are proportional to the square of the integral $\int \Psi_{v} x \Psi_{v} \mathrm{~d} x$ over all space. Use the relations between Hermite polynomials given in Table $9.1$ to show that the only permitted transitions are those for which $v^{\prime}=v \pm 1$ and evaluate the integral in these cases.

Name: We shall see in Chapter 13 that the intensities of spectroscopic transitions between the vibrational states of a molecule are proportional to the square of the integral ∫Ψv x Ψv d x over all space. Use the relations between Hermite polynomials given in Table 9.1 to show that the only permitted transitions are those for which v^'=v ± 1 and evaluate the integral in these cases.
Uploaded: 2023-03-13T15:27:43-08:00
Duration: 2 min 8 s
Channel: Sri K
Description: We shall see in Chapter 13 that the intensities of spectroscopic transitions between the vibrational states of a molecule are proportional to the square of the integral ∫Ψv x Ψv d x over all space. Use the relations between Hermite polynomials given in Table 9.1 to show that the only permitted transitions are those for which v^'=v ± 1 and evaluate the integral in these cases.

          We shall see in Chapter 13 that the intensities of spectroscopic transitions between the vibrational states of a molecule are proportional to the square of the integral $\int \Psi_{v} x \Psi_{v} \mathrm{~d} x$ over all space. Use the relations between Hermite polynomials given in Table $9.1$ to show that the only permitted transitions are those for which $v^{\prime}=v \pm 1$ and evaluate the integral in these cases.

Added by Christopher A.

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition

Instant Answer

Solved by Expert Sri K

03/13/2023

Step 1

Step 1: Recall the wavefunction for a harmonic oscillator in terms of Hermite polynomials: $\Psi_v(x) = N_v H_v(\alpha x) e^{-\frac{1}{2}(\alpha x)^2}$ where $N_v$ is the normalization constant, $H_v$ is the Hermite polynomial of order $v$, and $\alpha$ is a Show more…

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We shall see in Chapter 13 that the intensities of spectroscopic transitions between the vibrational states of a molecule are proportional to the square of the integral $\int \Psi_{v} x \Psi_{v} \mathrm{~d} x$ over all space. Use the relations between Hermite polynomials given in Table $9.1$ to show that the only permitted transitions are those for which $v^{\prime}=v \pm 1$ and evaluate the integral in these cases.