One-dimensional Schrödinger equation and its exact representation on a discrete lattice.

DOI10.1016/S0375-9601(96)00774-8zbMath1037.81531MaRDI QIDQ1968076

Miloslav Znojil

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) General spectral theory of ordinary differential operators (34L05) Discrete version of topics in analysis (39A12)

Related Items (2)

\(\mathcal{CPT}\)-symmetric discrete square well ⋮ Complete set of inner products for a discrete PT-symmetric square-well Hamiltonian

Cites Work

• The exact bound-state ansaetze as zero-order approximations in perturbation theory. II: An illustration: \(V(r)= r^2+ fr^2/ (1+gr^2)\)
• Stable forward shooting for eigenvalues and expectation values
• Double well model \(V(r)=ar^2+br^4+cr^6\) with \(a<0\) and perturbation method with triangular propagators
• A finite difference approach for the calculation of perturbed oscillator energies
• A new efficient method for calculating perturbation energies using functions which are not quadratically integrable
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