Conjecture on the interlacing of zeros in complex Sturm–Liouville problems
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Publication:2738193
DOI10.1063/1.1288247zbMath0994.34071arXivmath-ph/0005012OpenAlexW1969655067WikidataQ62599733 ScholiaQ62599733MaRDI QIDQ2738193
Stefan Boettcher, Van M. Savage, Carl M. Bender
Publication date: 30 August 2001
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0005012
Sturm-Liouville theory (34B24) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Oscillation theory of functional-differential equations (34K11) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)
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Cites Work
- Schrödinger operators with complex potential but real spectrum
- Variational ansatz for PT-symmetric quantum mechanics
- \(\mathcal P\mathcal T\)-symmetric harmonic oscillators
- Complex periodic potentials with real band spectra.
- Quasi-exactly solvable quartic potential
- Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
- A newPT-symmetric complex Hamiltonian with a real spectrum
- 𝓟𝓣-symmetric quantum mechanics
- Complex square well - a new exactly solvable quantum mechanical model
- SUSY QUANTUM MECHANICS WITH COMPLEX SUPERPOTENTIALS AND REAL ENERGY SPECTRA
