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Full-Text Articles in Quantum Physics
Quantum Mechanics With A Quartic Dispersion Law, Joanna Ruhl
Quantum Mechanics With A Quartic Dispersion Law, Joanna Ruhl
Graduate Masters Theses
Creation of three-dimensional matter waves, the three-dimensional analog of one-dimensional solitons, has been a goal of experimental physics for some time. A recent proposal has suggested that changing the dispersion law from quadratic to quartic for ultra cold atoms in a shaken lattice should allow for the creation of these objects. In this thesis, we develop the theoretical basis for quantum mechanics with a quartic dispersion law. The probability current functional is constructed from the corresponding time-dependent Schrödinger equation, and used to derive the junction conditions that connect the derivatives of the wavefunction on one side of a potential discontinuity …