International Journal of Modern Physics B · 2002 · 45 citations · 17 references
Natural SciencesPhysicsComputational MechanicsComputational PhysicsQuantum MechanicsComputational Quantum MechanicsNumerical Methods For Differential EquationsQuantum DynamicsSchrödinger EquationNumerical Solution Of The Schrödinger EquationStationary SolutionsTime-independent Schrödinger EquationWavefunction Solutions
A method is proposed for the quantum-mechanical determination of the eigenstates and eigenvalues of a particle (e.g. an electron) in a potential of general shape. For such systems the method allows one to calculate the exact solutions of the stationary Schrödinger equation. For the application of this method any well-known reference system is needed. A transition from the stationary reference system to the stationary system under investigation is performed by means of the time-dependent Schrödinger equation. The results are compared with various standard methods; alternative numerical methods will be discussed critically.
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