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SUSY-based variational method for the anharmonic oscillator. (English) Zbl 0941.81526
Summary: Using a newly suggested algorithm of Gozzi, Reuter and Thacker for calculating the excited states of one-dimensional systems, we determine approximately the eigenvalues and eigenfunctions of the anharmonic oscillator, described by the Hamiltonian \(H=\frac 12 p^2+gx^4\). We use ground state post-Gaussian trial wave functions of the form \(\Psi(x) = N \exp(-b|x|^{2n})\), where \(n\) and \(b\) are continuous variational parameters. This algorithm is based on the hierarchy of Hamiltonians related by supersymmetry (SUSY) and the factorization method. We find that our two-parameter family of trial wave functions yields excellent energy eigenvalues and wave functions for the first few levels of the anharmonic oscillator.

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81-04 Software, source code, etc. for problems pertaining to quantum theory
81Q60 Supersymmetry and quantum mechanics
Full Text: DOI
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