Pavel Stránský
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Last updated: 19.11.2024

Errors in the calculation of the eigenstates

B
0.240.621.09
Basis size
150250
hbar
0.010.020.050.1
Trace of the Hamiltonian matrix
Figure 1: Trace of the Hamiltonian matrix
The Hamiltonian matrix is constructed in the oscillator basis with a parameterA0. The best value is A0=A0min/2 (it roughly corresponds with the position of the minimum of the trace).
Convergence of energy levels
Figure 2: Energy versus the ordering number of the energy level
Various lines correspond to various A0. The lower the curve the better. The convergence is achieved if the energies of several successive A0 have the same value.
Convergence of eigenvectors 0
Convergence of eigenvectors 1
Convergence of eigenvectors 2
Convergence of eigenvectors 3
Convergence of eigenvectors 4
Convergence of eigenvectors 5
Convergence of eigenvectors 6
Convergence of eigenvectors 7
Convergence of eigenvectors 8
Convergence of eigenvectors 9
Figure 3: Eigenvector convergence
A sum of the absolute values of the last 100 components of the eigenvectors. The convergence is achieved if this sum is almost zero.
Convergence of Peres lattices 0
Convergence of Peres lattices 1
Convergence of Peres lattices 2
Convergence of Peres lattices 3
Convergence of Peres lattices 4
Convergence of Peres lattices 5
Convergence of Peres lattices 6
Convergence of Peres lattices 7
Convergence of Peres lattices 8
Convergence of Peres lattices 9
Figure 4: Peres lattices
The convergence is achieved for those states whose lattice points are at same places for various successive values of A0.