Using ab initio calculations of great accuracy, we have obtained a polynomial potential function for the inversion coordinate of NH3. The vibrational spectrum is obtained by solving numerically the Schrodinger equation for this potential function. The same potential function is used to generate the vibrational spectrum of the isotopic species ND3. Theoretical results are discussed in comparison with experimental and semiempirical inversion frequencies. We generated graphs of the eigenfunctions for this system.
An algebraic approach is proposed to calculate the Franck-Condon factors for the Morse potential of diatomic molecules. The Morse oscillator is approximated by means of a fourth-order anharmonic oscillator. In the second-quantized formalism, this anharmonic Hamiltonian is diagonalized by way of the Bogoliubov-Tyablikov transformation. The Franck-Condon factors are estimated using the harmonic frequency equivalent and the recurrence relations for the FranckCondon factors of the harmonic oscillator. Overlap integrals are shown for three band systems and compared with values calculated with an RKR potential. Excellent agreement is achieved.
ABSTRACT:The solution of the Schrö dinger equation for the linear time-dependent potential has recently been the subject of several publications. In this report, we show this is one of the few systems that leads to a solvable Lie algebra. In fact, we consider a more general problem where the linear time-dependent potential is only a particular case. The solution is found by using the well-known theorem of Wei-Norman.
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