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Solving Schrodinger equation numerically pt 1
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Part 1
An exact three-particle solver (but without relativstic effects). No basis functions. Instead discretization in 3D space using finite difference expressions is used. The eigenvalue and wavefunction is determined by using a fast and robust particle method. The corresponding Hamiltonian matrix often become nonsymmetrical due to mathematical transformations or nonsymmetrical finite difference expressions. This makes it troublesome for the conjugate gradient method which only deals with a symmetrical matrix and it also requires all eigenvalues to be positive. The particle method has no such restrictions (other than that the eigenvalues must be real).
An exact three-particle solver (but without relativstic effects). No basis functions. Instead discretization in 3D space using finite difference expressions is used. The eigenvalue and wavefunction is determined by using a fast and robust particle method. The corresponding Hamiltonian matrix often become nonsymmetrical due to mathematical transformations or nonsymmetrical finite difference expressions. This makes it troublesome for the conjugate gradient method which only deals with a symmetrical matrix and it also requires all eigenvalues to be positive. The particle method has no such restrictions (other than that the eigenvalues must be real).
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