using System; using Science.Mathematics; using L = Science.Physics.QuantumMechanics; namespace ScienceTest.PhysicsTest.QuantumMechanicsTest { /// /// We solve the differential equation : R(r) = r^|m| \Psi(r) /// -0.5{\Psi''(r) + (2m+1)/r\Psi'(r)} + V(r)\Psi(r) = E\Psi(r) /// public class SchroedingerEq2DTest { public SchroedingerEq2DTest() { } private string result; public string Result { get{return result;} } public void Compute() { L.SchroedingerEquation2D equation = new L.SchroedingerEquation2D(); Function.ToLastType func = new Function.ToLastType(V); equation.PotentialEnergy = func; equation.RadialBoundary = 12.0; // radius should be large enough for wavefunction to be 0 equation.EnergyGuess = 4.87; // change as you wish equation.SlopeGuess = -5.0E-15; // change to adjust \Psi(r) equation.ValueAtOriginGuess = 12.0; // change as you wish equation.Solve(); for(int k = 0; k < equation.WaveFunction.Length; k++) result += Convert.ToString(equation.WaveFunctionRadialCoordinate[k])+"\t" // position + Convert.ToString(equation.WaveFunction[k])+"\t" // value + Convert.ToString(equation.WaveFunctionDerivative[k])+"\r\n"; // derivative result += "Energy="+Convert.ToString(equation.Energy)+"\r\n"; } private double V(double r) { return 0.5*r*r; // change as you wish } } } /* 0 9.18292019469931 0 0.03 9.09634686060015 -5.75788598625799 0.06 8.83907958078858 -11.3526903542612 0.09 8.41839880704013 -16.6264979550799 0.12 7.84618218731391 -21.4315528409577 0.15 7.13852896467453 -25.6349096140471 0.18 6.31525192164329 -29.1225877294761 0.21 5.39925390505727 -31.8030905038433 0.24 4.41580979149402 -33.6101728046878 0.27 3.39177784974716 -34.5047676240595 0.3 2.35476671771382 -34.4760110164362 0.33 1.33228556133219 -33.5413361545907 0.36 0.350905379090139 -31.745639398053 0.39 -0.564541151165154 -29.1595531281496 0.42 -1.39169539060002 -25.8768905441659 0.45 -2.11132051293138 -22.0113555615879 0.48 -2.70784099425934 -17.6926354247888 0.51 -3.16975732268997 -13.0620137986289 0.54 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