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- Title
Quantum star-graph analogues of -symmetric square wells.
- Authors
Znojil, Miloslav
- Abstract
We recall the solvable -symmetric quantum square well on an interval of x ∈ (- L, L) := (with an α-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a q-pointed equilateral star graph endowed with the simplest complex-rotation-symmetric external α-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that ( i) at any integer q = 2, 3, ..., there exists the same q-independent and infinite subfamily of the real energies, and ( ii) at any special q = 2, 6, 10, ..., there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finally proposed.
- Subjects
SYMMETRY (Physics); STAR graphs (Graph theory); QUANTUM theory; BOUNDARY value problems; EIGENVALUES; PROBLEM solving; HILBERT space
- Publication
Canadian Journal of Physics, 2012, Vol 90, Issue 12, p1287
- ISSN
0008-4204
- Publication type
Article
- DOI
10.1139/p2012-107