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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.

MSC:
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
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