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- Laughlin_wavefunction abstract "In condensed matter physics, the Laughlin wavefunction is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium background when the filling factor (Quantum Hall effect) of the lowest Landau level is where is an odd positive integer. It was constructed to explain the observation of the fractional quantum Hall effect, and predicted the existence of additional states as well as quasiparticle excitations with fractional electric charge , both of which were later experimentally observed. Laughlin received one third of the Nobel Prize in Physics in 1998 for this discovery. Being a trial wavefunction, it is not exact, but qualitatively, it reproduces many features of the exact solution and quantitatively, it has very high overlaps with the exact ground state for small systems.If we ignore the jellium and mutual Coulomb repulsion between the electrons as a zeroth order approximation, we have an infinitely degenerate lowest Landau level (LLL) and with a filling factor of 1/n, we'd expect that all of the electrons would lie in the LLL. Turning on the interactions, we can make the approximation that all of the electrons lie in the LLL. If is the single particle wavefunction of the LLL state with the lowest orbital angular momentum, then the Laughlin ansatz for the multiparticle wavefunction iswhere position is denoted byand normalization[citation needed]in (Gaussian units)and and are coordinates in the xy plane. Here is Planck's constant, is the electron charge, is the total number of particles, and is the magnetic field, which is perpendicular to the xy plane. The subscripts on z identify the particle. In order for the wavefunction to describe fermions, n must be an odd integer. This forces the wavefunction to be antisymmetric under particle interchange. The angular momentum for this state is .".
- Laughlin_wavefunction thumbnail 101017_Expectation_value_vs_l.jpg?width=300.
- Laughlin_wavefunction wikiPageID "15112730".
- Laughlin_wavefunction wikiPageRevisionID "585421699".
- Laughlin_wavefunction hasPhotoCollection Laughlin_wavefunction.
- Laughlin_wavefunction subject Category:Condensed_matter_physics.
- Laughlin_wavefunction subject Category:Hall_effect.
- Laughlin_wavefunction subject Category:Quantum_phases.
- Laughlin_wavefunction comment "In condensed matter physics, the Laughlin wavefunction is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium background when the filling factor (Quantum Hall effect) of the lowest Landau level is where is an odd positive integer.".
- Laughlin_wavefunction label "Laughlin wavefunction".
- Laughlin_wavefunction sameAs m.03hhtpt.
- Laughlin_wavefunction sameAs Q6498183.
- Laughlin_wavefunction sameAs Q6498183.
- Laughlin_wavefunction wasDerivedFrom Laughlin_wavefunction?oldid=585421699.
- Laughlin_wavefunction depiction 101017_Expectation_value_vs_l.jpg.
- Laughlin_wavefunction isPrimaryTopicOf Laughlin_wavefunction.
