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All Journal Jurnal Teras Fisika : Teori, Modeling, dan Aplikasi Fisika
Fima Ardianto Putra
Universitas Jenderal Soedirman
Materials Science & Nanotechnology

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De Broglie Wave Analysis of the Heisenberg Uncertainty Minimum Limit under the Lorentz Transformation Fima Ardianto Putra
Jurnal Teras Fisika: Teori, Modeling, dan Aplikasi Fisika Vol 1 No 2 (2018): Jurnal Teras Fisika: Teori, Modeling, dan Aplikasi Fisika
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (244.15 KB) | DOI: 10.20884/1.jtf.2018.1.2.1008

Abstract

A simple analysis using differential calculus has been done to consider the minimum limit of the Heisenberg uncertainty principle in the relativistic domain. An analysis is made by expressing the form of and based on the Lorentz transformation, and their corresponding relation according to the de Broglie wave packet modification. The result shows that in the relativistic domain, the minimum limit of the Heisenberg uncertainty is p x ћ/2 and/or E t ћ/2, with is the Lorentz factor which depend on the average/group velocity of relativistic de Broglie wave packet. While, the minimum limit according to p x ћ/2 or E t ћ/2, is the special case, which is consistent with Galilean transformation. The existence of the correction factor signifies the difference in the minimum limit of the Heisenberg uncertainty between relativistic and non-relativistic quantum. It is also shown in this work that the Heisenberg uncertainty principle is not invariant under the Lorentz transformation. The form p x ћ/2 and/or E t ћ/2 are properly obeyed by the Klein-Gordon and the Dirac solution. Key words: De Broglie wave packet, Heisenberg uncertainty, Lorentz transformation, and minimum limit.
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