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WAVE PACKET SOLUTIONS OF THE TIME DEPENDENT SCHROEDINGER EQUATION.

Iowa (USA) Ames Lab., T. A. Weber, C. L. Hammer

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Abstract

The wave packet solutions of the non-relativistic time dependent Schroedinger equation are considered for cases where the usual scattering approximations have doubtful or no validity.The results, although very similar in form to the results of the usual Lippmann -Schwinger formalism, are exact, rather than approximate, even when the incident wave packet is a finite distance from the scattering center.Consequently, solutions that involve time dependence, such as decaying states, are included in the formalism.The formalism is first developed for the one dimensional case and then generalized to three dimensions. DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the

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The wave packet solutions of the non-relativistic time dependent Schroedinger equation are considered for cases where the usual scattering approximations have doubtful or no validity.The results, although very similar in form to the results of the usual Lippmann -Schwinger formalism, are exact, rather than approximate, even when the incident wave packet is a finite distance from the scattering center.Consequently, solutions that involve time dependence, such as decaying states, are included in the formalism.The formalism is first developed for the one dimensional case and then generalized to three dimensions. DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the

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Available abstract

The wave packet solutions of the non-relativistic time dependent Schroedinger equation are considered for cases where the usual scattering approximations have doubtful or no validity.The results, although very similar in form to the results of the usual Lippmann -Schwinger formalism, are exact, rather than approximate, even when the incident wave packet is a finite distance from the scattering center.Consequently, solutions that involve time dependence, such as decaying states, are included in the formalism.The formalism is first developed for the one dimensional case and then generalized to three dimensions. DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the

Key concepts: Wave packet, Scattering, Physics, Schrödinger equation, Scattering theory, Formalism (music), Quantum, Inelastic scattering

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