/// <summary>
/// Calculates the value of a (freely evolving) Gaussian wavepacket at a given location and time.
/// </summary>
public static Complex FreeGaussianWavePacketValue(float x, float y, float z, float t,
Vec3 initialCenter, Vec3 initialWidth, Vec3 avgMomentum, float mass)
{
Complex I = Complex.I;
Complex effSigmaXSq = initialWidth.X * initialWidth.X + I * (t / mass);
Complex effSigmaYSq = initialWidth.Y * initialWidth.Y + I * (t / mass);
Complex effSigmaZSq = initialWidth.Z * initialWidth.Z + I * (t / mass);
float xRel = x - initialCenter.X - avgMomentum.X * t / mass;
float yRel = y - initialCenter.Y - avgMomentum.Y * t / mass;
float zRel = z - initialCenter.Z - avgMomentum.Z * t / mass;
float avgMomentumSq = avgMomentum.NormSq();
Complex expArg = I * (x * avgMomentum.X + y * avgMomentum.Y + z * avgMomentum.Z) - I * t * avgMomentumSq / (2 * mass) -
(xRel * xRel) / (2 * effSigmaXSq) - (yRel * yRel) / (2 * effSigmaYSq) - (zRel * zRel) / (2 * effSigmaZSq);
float rootPi = (float)Math.Sqrt(Math.PI);
Complex normX = Complex.Sqrt(initialWidth.X / (rootPi * effSigmaXSq));
Complex normY = Complex.Sqrt(initialWidth.Y / (rootPi * effSigmaYSq));
Complex normZ = Complex.Sqrt(initialWidth.Z / (rootPi * effSigmaZSq));
Complex wfVal = normX * normY * normZ * Complex.Exp(expArg);
return(wfVal);
}
