Journal ArticleDOI
Polynomial potentials and a hidden symmetry of the Hill-determinant eigenvalue method
TLDR
For the potential V (x ) = g 1 x 2 + g 2 x 4 + g 3 x 6 and its polynomial generalizations, the true and false energies of Killingbeck may both be interpreted as physical, corresponding to the two different forms of the potential.Citations
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Exact solutions and ladder operators for a new anharmonic oscillator
TL;DR: In this article, a new anharmonic oscillator was proposed and the exact solutions of the Schrodinger equation with this oscillator were presented, and the ladder operators were established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions.
Journal ArticleDOI
The Hill determinant method in application to the sextic oscillator: limitations and improvement
TL;DR: Using the sextic anharmonic oscillator a chi 2+b chi 4+c chi 6 as a testing ground it was shown why the Hill determinant method has a limited range of applicability.
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Classification of oscillators in the Heisenberg-matrix representation
TL;DR: For an arbitrary finite and not too singular (presumably, phenomenological) superposition of potentials rdelta with rational exponents, this article solved the old problem of conversion of the corresponding differential Schrodinger bound-state problem into its matrix equivalent with the minimalized number L of non-zero diagonals.
Journal ArticleDOI
Failure of the Hill determinant method for the sextic anharmonic oscillator
M Tater,A V Turbiner +1 more
TL;DR: In this article, an extended analysis of eigenvalues and wavefunctions resulting from the Hill determinant method is carried out for the one-dimensional sextic anharmonic oscillator.
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Spiked and -symmetrized decadic potentials supporting elementary N-plets of bound states
TL;DR: In this article, it was shown that the potential well V(x) = x10 + ax8 + bx6 + cx4 + dx2 + f/x2 with a central spike possesses arbitrary finite multiplets of elementary exact bound states.
References
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Journal ArticleDOI
Anharmonic oscillator and the analytic theory of continued fractions
TL;DR: In this paper, the authors study anharmonic oscillators of the type $a{x}^{2}+b{x]^{4}+c{x})6} using the theory of continued fractions and obtain the analytic structure of the Green's function in the complex plane of this coupling constant.
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The rotating harmonic oscillator eigenvalue problem. I. Continued fractions and analytic continuation
TL;DR: In this paper, the continued fraction approach to the solution of the rotating harmonic oscillator eigenvalue problem is examined in detail, and it is shown how one may obtain eigen value information only from an analytic continuation of the continued fractions accomplished with the aid of modified approximants.
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Accurate finite difference eigenvalues
TL;DR: Perturbation theory is used to construct a family of high order shooting methods for finding Schrodinger equation eigenvalues as mentioned in this paper, which is used for finding high order Eigenvalues.
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Analytic continued fraction technique for bound and confined states for a class of confinement potentials
D P Datta,S Mukherjee +1 more
TL;DR: In this paper, the convergence and analyticity of the infinite continued fraction representation of the Green function for a class of confinement potentials in terms of the Coulomb-like coupling constant were investigated.