Quasi-exactly solvable quartic potentials with centrifugal and Coulombic terms

Abstract

PT symmetric complex potential V(r) = - r^4 + i a r^3 + b r^2 + i c r + i d/r + e/r^2 is studied. Arbitrarily large multiplets of its closed bound-state solutions with real energies are shown obtainable quasi-exactly (i.e., with a certain relationship between their charges and energies) from a single underlying finite-dimensional secular equation.

13 pages, 1 figure, submitted to J. Phys. A: Math. Gen

References in corpus (5)

• PT -symmetric harmonic oscillators
• A new PT symmetric complex Hamiltonian with a real spectra
• Exact solution for Morse oscillator in PT-symmetric quantum mechanics
• Shape invariant potentials with PT symmetry
• Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

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• Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthen Potential by the Nikiforov-Uvarov Method
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• Coupled-channel version of PT-symmetric square well
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• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
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• Solvable PT symmetric Hamiltonians
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• Quasi-exact minus-quartic oscillators in strong-core regime
• Quasi-exactly solvable cases of the N-dimensional symmetric quartic anharmonic oscillator
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