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quantum potential : ウィキペディア英語版
quantum potential
The quantum potential or quantum potentiality is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952.
Initially presented under the name ''quantum-mechanical potential'', subsequently ''quantum potential'', it was later elaborated upon by Bohm and Basil Hiley in its interpretation as an information potential which acts on a quantum particle. It is also referred to as ''quantum potential energy'', ''Bohm potential'', ''quantum Bohm potential'' or ''Bohm quantum potential''.
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In the framework of the de Broglie–Bohm theory, the quantum potential is a term within the Schrödinger equation which acts to guide the movement of quantum particles. The quantum potential approach introduced by Bohm〔 ((full text ))〕〔 ((full text ))〕 provides a formally more complete exposition of the idea presented by Louis de Broglie: de Broglie had postulated in 1926 that the wave function represents a pilot wave which guides a quantum particle, but had subsequently abandoned his approach due to objections raised by Wolfgang Pauli. The seminal articles of Bohm in 1952 introduced the quantum potential and included answers to the objections which had been raised against the pilot wave theory.
The Bohm quantum potential is closely linked with the results of other approaches, in particular relating to work by Erwin Madelung of 1927 and to work by Carl Friedrich von Weizsäcker of 1935.
Building on the interpretation of the quantum theory introduced by Bohm in 1952, David Bohm and Basil Hiley in 1975 presented how the concept of a ''quantum potential'' leads to the notion of an "unbroken wholeness of the entire universe", proposing that the fundamental new quality introduced by quantum physics is nonlocality.〔D. Bohm, B. J. Hiley: ''On the intuitive understanding of nonlocality as implied by quantum theory'', Foundations of Physics, Volume 5, Number 1, pp. 93-109, 1975, ((abstract ))〕
== Quantum potential as part of the Schrödinger equation ==
The Schrödinger equation
:
i \hbar \frac = \left( - \frac \nabla^2 +V \right)\psi \quad

is re-written using the polar form for the wave function \quad \psi = R \exp i S / \hbar with real-valued functions R and S, where R is the amplitude (absolute value) of the wave function \psi and S/\hbar its phase. This yields two equations: from the imaginary and real part of the Schrödinger equation follow the continuity equation and the quantum Hamilton-Jacobi equation, respectively.〔〔David Bohm, Basil Hiley: ''The Undivided Universe: An Ontological Interpretation of Quantum Theory'', Routledge, 1993, ISBN 0-415-06588-7, therein Chapter 3.1. ''The main points of the causal interpretation'', p. 22–(23 )〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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