Since the introduction of a series of methods for solving the time-dependent Schrödinger equation... more Since the introduction of a series of methods for solving the time-dependent Schrödinger equation (TDSE) in the 80s of the last centry, such as the Fourier transform, the split operator (SO), the Chebyshev polynomial propagator, and complex absorbing potential, investigation of the molecular dynamics within quantum mechanics principle have become popular. In this paper, the application of the time-dependent wave packet (TDWP) method using high-order SO propagators in hyperspherical coordinates for solving triatomic reactive scattering was investigated. The fast sine transform was applied to calculate the derivatives of the wave function of the radial degree of freedom. These high-order SO propagators are examined in different forms, i.e., TVT (Kinetic-Potential-Kinetic) and VTV (Potential-Kinetic-Potential) forms with three typical triatomic reactions, H + H 2 , O + O 2 and F + HD. A little difference has been observed among the performances of high-order SO propagators in the TVT and VTV representations in the hyperspherical coordinate. For obtaining total reaction probabilities with 1% error, some of the S class high-order SO propagators, which have symmetric forms, are more efficient than second order SO for reactions involving long lived intermediate states. High order SO propagators are very efficient for obtaining total reaction probabilities.
Wittgenstein and the Practice of Philosophy introduces Wittgenstein's philosophy to senior un... more Wittgenstein and the Practice of Philosophy introduces Wittgenstein's philosophy to senior undergraduates and graduate students. Its pedagogical premise is that the best way to understand Wittgenstein's thought is to take seriously his methodological remarks. Its interpretive premise is that those methodological remarks are the natural result of Wittgenstein's rejection of his early view of the ground of value, including semantic value or meaning, as something that must lie "outside the world." This metaphysical view of meaning is replaced in his transitional writings with a kind of conventionalism, according to which meaning is made possible by the existence of grammatical conventions that are implicit in our linguistic practices. The implicit nature of these conventions makes us vulnerable to a special kind of confusion that results from lacking a clear view of the norms that underlie our linguistic practices. This special confusion is characteristic of philo...
Since the introduction of a series of methods for solving the time-dependent Schrödinger equation... more Since the introduction of a series of methods for solving the time-dependent Schrödinger equation (TDSE) in the 80s of the last centry, such as the Fourier transform, the split operator (SO), the Chebyshev polynomial propagator, and complex absorbing potential, investigation of the molecular dynamics within quantum mechanics principle have become popular. In this paper, the application of the time-dependent wave packet (TDWP) method using high-order SO propagators in hyperspherical coordinates for solving triatomic reactive scattering was investigated. The fast sine transform was applied to calculate the derivatives of the wave function of the radial degree of freedom. These high-order SO propagators are examined in different forms, i.e., TVT (Kinetic-Potential-Kinetic) and VTV (Potential-Kinetic-Potential) forms with three typical triatomic reactions, H + H 2 , O + O 2 and F + HD. A little difference has been observed among the performances of high-order SO propagators in the TVT and VTV representations in the hyperspherical coordinate. For obtaining total reaction probabilities with 1% error, some of the S class high-order SO propagators, which have symmetric forms, are more efficient than second order SO for reactions involving long lived intermediate states. High order SO propagators are very efficient for obtaining total reaction probabilities.
Wittgenstein and the Practice of Philosophy introduces Wittgenstein's philosophy to senior un... more Wittgenstein and the Practice of Philosophy introduces Wittgenstein's philosophy to senior undergraduates and graduate students. Its pedagogical premise is that the best way to understand Wittgenstein's thought is to take seriously his methodological remarks. Its interpretive premise is that those methodological remarks are the natural result of Wittgenstein's rejection of his early view of the ground of value, including semantic value or meaning, as something that must lie "outside the world." This metaphysical view of meaning is replaced in his transitional writings with a kind of conventionalism, according to which meaning is made possible by the existence of grammatical conventions that are implicit in our linguistic practices. The implicit nature of these conventions makes us vulnerable to a special kind of confusion that results from lacking a clear view of the norms that underlie our linguistic practices. This special confusion is characteristic of philo...
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