On the Use of B-Splines as Ritz Variational Basis Functions to Solve the Schrodinger Equation (TISE) for a constrained free Quantum Particle
Keywords:B-Splines, Variational basis, TISE, free particle, Gauss Legendre quadrature, Collocation, Eigen solution
B-Splines as piecewise adaptation of Bernstein polynomials (aka, B-polys) are widely used as Ritz variational basis functions in solving many problems in the fields of quantum mechanics and atomic physics. In this paper they are used to solve the 1-D stationary Schrodinger equation (TISE) for a free quantum particle subject to a fixed domain length by using the Python software SPLIPY with different sets of computation parameters. In every case it was found that over 60 percent of energy levels had excellent accuracy thereby proving that the use of B-spline collocation is a preferred method.
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Access “SPLIPY 1.3.1” from https://github.com/sintefmath/Splipy/
Access “Bspline.py” from https://github.com/johntfoster/bspline
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