A rotational‐dependent analytical solution to the dissociative state: Application to b 3Σ+u state of H2
| Autor: | Lue-yung Chow Chiu, Edward E. LaFleur |
|---|---|
| Rok vydání: | 1986 |
| Předmět: |
Physics
Chebyshev polynomials Confluent hypergeometric function General Physics and Astronomy WKB approximation Schrödinger equation symbols.namesake Quantum mechanics symbols Physical and Theoretical Chemistry Wave function Asymptotic expansion Convergent series Mathematical physics Morse potential |
| Zdroj: | The Journal of Chemical Physics. 84:2150-2157 |
| ISSN: | 1089-7690 0021-9606 |
| DOI: | 10.1063/1.450376 |
| Popis: | The rotational‐dependent potential for a dissociative state is represented by U(r)=U0+B1/r +B2/r2+[N(N+1)−Λ2]/2Mr2. An analytical solution ψE(r) of the Schrodinger radial equation, valid for all regions of internuclear distance r and energy E, is obtained in terms of confluent hypergeometric function of the complex arguments. The solution is evaluated by expanding the confluent hypergeometric function onto a basis set of shifted Chebyshev polynomials. The expansion coefficients are recovered by a backward recursion technique. The summation process of Chebyshev polynomials converts a slowly convergent series or a divergent asymptotic series into a rapidly convergent one. The solution thus obtained is applied to calculate the vibrational wave function of the dissociative b 3Σ+u state of H2 to compare with the previous semiclassical WKB wave function. The solution of the rotational‐corrected Morse potential is used for the upper bound c 3Πu state. The bound‐continuum Frank–Condon overlap amplitude is compute... |
| Databáze: | OpenAIRE |
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