an:01399645
Zbl 0941.81526
Cooper, Fred; Dawson, John; Shepard, Harvey
SUSY-based variational method for the anharmonic oscillator
EN
Phys. Lett., A 187, No. 2, 140-144 (1994).
00063164
1994
j
81Q05 81-04 81Q60
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.