A Soluble Model for Scattering and Decay in Quaternionic Quantum Mechanics I: Decay
نویسنده
چکیده
The Lee-Friedrichs model has been very useful in the study of decay-scattering systems in the framework of complex quantum mechanics. Since it is exactly soluble, the analytic structure of the amplitudes can be explicitly studied. It is shown in this paper that a similar model, which is also exactly soluble, can be constructed in quaternionic quantum mechanics. The problem of the decay of an unstable system is treated here. The use of the Laplace transform, involving quaternion-valued analytic functions of a variable with values in a complex subalgebra of the quaternion algebra, makes the analytic properties of the solution apparent; some analysis is given of the dominating structure in the analytic continuation to the lower half plane. A study of the corresponding scattering system will be given in a succeeding paper.
منابع مشابه
A Soluble Model for Scattering and Decay in Quaternionic Quantum Mechanics Ii: Scattering
In a previous paper, it was shown that a soluble model can be constructed for the description of a decaying system in analogy to the Lee-Friedrichs model of complex quantum theory. It is shown here that this model also provides a soluble scattering theory , and therefore constitutes a model for a decay scattering system. Generalized second resolvent equations are obtained for quaternionic scatt...
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