Effective Potential from the Generalized Time-Dependent Schrödinger Equation
نویسندگان
چکیده
منابع مشابه
Effective Potential from the Generalized Time-Dependent Schrödinger Equation
We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potent...
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Article history: Received 3 November 2009 Accepted 21 November 2009 Available online xxxx
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81Q05 Synonyms or related entries control of quantum dynamics by electromagnetic radiation; laser control of chemical reactions; control of spin systems; control in Nuclear Magnetic Resonance; construction of logic gates for quantum computers Definition Quantum control is the control, at the quantum level, of the state or dynamical evolution of some quantum system by means of electromagnetic ra...
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An adaptive numerical method for solution of the time-dependent Schrödinger equation is presented. By using an interpolating wavelet transform the number of used points can be reduced, constructing an adaptive sparse point representation. Two di erent discretisation approaches are studied in 1D ; one point-based and one based on equidistant blocks. Due to the nature of the wavelet transform a s...
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We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schrödinger equation. The generalization yields numerical solutions accurate to order (Deltax)2r-1 in space and (Deltat)2M in time for any positive integers r and M, while CN employ r=M=1. We note dramatic improvement in the attainable precision (circa ten or greater o...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2016
ISSN: 2227-7390
DOI: 10.3390/math4040059