page_title: Quantum potential
section_title: Properties
hierarchical_section_title: Quantum potential / Properties
context_page_description: 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.
  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 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.
context_section_description: Hiley emphasised several aspects that regard the quantum potential of a quantum particle:
  it is derived mathematically from the real part of the Schrödinger equation under polar decomposition of the wave function, is not derived from a Hamiltonian or other external source, and could be said to be involved in a self-organising process involving a basic underlying field;
  it does not change if  is multiplied by a constant, as this term is also present in the denominator, so that  is independent of the magnitude of  and thus of field intensity; therefore, the quantum potential fulfils a precondition for nonlocality: it need not fall off as distance increases;
  it carries information about the whole experimental arrangement in which the particle finds itself.
  In 1979, Hiley and his co-workers Philippidis and Dewdney presented a full calculation on the explanation of the two-slit experiment in terms of Bohmian trajectories that arise for each particle moving under the influence of the quantum potential, resulting in the well-known interference patterns.
  Also the shift of the interference pattern which occurs in presence of a magnetic field in the Aharonov–Bohm effect could be explained as arising from the quantum potential.
caption: Schematic of double-slit experiment in which Aharonov–Bohm effect can be observed: electrons pass through two slits, interfering at an observation screen, and the interference pattern undergoes a shift when a magnetic field B is turned on in the cylindrical solenoid.