Kajian Integral Lintasan Levy dalam Mekanika Kuantum Fraksional untuk Membentuk Persamaan Schrodinger Fraksional

Risenologi : Jurnal Sains, Teknologi, Sosial, Pendidikan, dan Bahasa

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Title Kajian Integral Lintasan Levy dalam Mekanika Kuantum Fraksional untuk Membentuk Persamaan Schrodinger Fraksional
 
Creator Halim, Chandra
Rosyid, M. Farchani
 
Subject Lévy, Quantum Mechanics, Schrödinger.
 
Description The implementation of Lévy path integral generated by Lévy stochastic process on fractional Schrödinger equation has been investigated in the framework of fractional quantum mechanics. As the comparison, the implementation of Feynmann path integral generated by Wiener stochastic process on Schrödinger equation also has been investigated in the framework of standard quantum mechanics. There are two stochastic processes. There are Lévy stochastic and Wiener stochastic process. Both of them are able to produce fractal. In fractal’s concept, there is a value known as fractal dimension. The implementation of fractal dimension is the diffusion equation obtained by using Fokker Planck equation. In this paper, Lévy and Wiener fractal dimension have been obtained. There are  for Lévy and 2 for Wiener/Brown fractal dimension. Fractional quantum mechanics is generalization of standard quantum mechanics. A fractional quantum mechanics state is represented by wave function from fractional Schrödinger equation. Fractional Schrödinger equation is obtained by using kernel of Lévy path integral generated by Lévy stochastic process. Otherwise, standard quantum mechanics state is represented by wave function from standard Schrödinger equation. Standard Schrödinger equation is obtained by using kernel of Feynmann path integral generated by Wiener/Brown stochastic process.  Both Lévy and Feynmann Kernel have been investigated and the outputs are the Fourier Integral momentum phase of those kernels. We find that the forms of those kernels have similiraty. Therefore, we obtain Schrödinger equation from Lévy and Feynmann Kernel and also the comparison of Lévy energy in fractional quantum mechanics and particle energy in standard quantum mechanics.
 
Publisher Lembaga Penelitian Kelompok Peneliti Muda Universitas Negeri Jakarta
 
Date 2020-04-29
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Peer-reviewed Article
 
Format application/pdf
 
Identifier http://ejurnal.kpmunj.org/index.php/risenologi/article/view/80
10.47028/j.risenologi.2020.51.80
 
Source Risenologi; Vol. 5 No. 1 (2020): Risenologi (Jurnal Sains, Teknologi, Sosial, Pendidikan, dan Bahasa); 80-86
2720-9571
2502-5643
 
Language eng
 
Relation http://ejurnal.kpmunj.org/index.php/risenologi/article/view/80/77
 
Rights Copyright (c) 2020 Risenologi : Jurnal Sains, Teknologi, Sosial, Pendidikan, dan Bahasa
 

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