1999/06/30 by Miloslav Znojil · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Anharmonicity #Eigenvalues and eigenvectors #Hermitian matrix #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Photonic Systems #Operator (biology) #Physics #Positive-definite matrix #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #quant-ph
paper · pdf · doi:10.1088/0305-4470/32/42/313
published as J.Phys.A32:7419-7428,1999 · 18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appear
arxiv created 1999/09/07 · openalex publication_date 1999/10/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The -symmetric differential Schrödinger equation H = E with the operator H = H ( x ) = p 2 + ax 4 +i x 3 + cx 2 +i x H * (- x ) on L 2 (- , ) is studied. At a > 0 it is rearranged as a linear algebraic diagonalization. With rigorous proof, our non-variational construction of bound states offers an infinite-dimensional analogue to the recent finite-dimensional quasi-exact solution available at the less common a <0.