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Analytically solvable Hamiltonians for quantum two-level systems and their dynamics

2014

A simple systematic way of obtaining analytically solvable Hamiltonians for quantum two-level systems is presented. In this method, a time-dependent Hamiltonian and the resulting unitary evolution operator are connected through an arbitrary function of time, furnishing us with new analytically solvable cases. The method is surprisingly simple, direct, and transparent and is applicable to a wide class of two-level Hamiltonians with no involved constraint on the input function. A few examples illustrate how the method leads to simple solvable Hamiltonians and dynamics.

Time-dependent HamiltonianStatistics and ProbabilitySolvable modelGeneral Physics and AstronomyInput functionStatistical and Nonlinear PhysicsQuantum two-level systemArbitrary functionSettore FIS/03 - Fisica Della MateriaPhysics and Astronomy (all)symbols.namesakeQuantum two-level system; Solvable model; Time-dependent Hamiltonian; Mathematical Physics; Physics and Astronomy (all); Statistical and Nonlinear Physics; Modeling and Simulation; Statistics and ProbabilityModeling and SimulationQuantum mechanicssymbolsMathematical PhysicHamiltonian (quantum mechanics)Unitary evolutionsolvable model quantum two-level system time-dependent HamiltonianQuantumMathematical PhysicsStatistical and Nonlinear PhysicMathematicsMathematical physicsJournal of Physics A: Mathematical and Theoretical
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