کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1899484 1045063 2006 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for wigner functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for wigner functions
چکیده انگلیسی

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations, in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Reports on Mathematical Physics - Volume 57, Issue 1, February 2006, Pages 17-26