\$title An Application from Quantum Mechanics (QUANTUM,SEQ=300) \$onText An application from quantum mechanics: Find energy eigenvalues of the anharmonic oscillator with g = 1 in the Gaussian and Post-Gaussian variational methods. Erwin Kalvelagen, May 2004 Ogura, A, Post-Gaussian variational method for quantum anharmonic oscillator, 1999. Laboratory of Physics, College of Science and Technology, Nihon University,arXiv:physics/9905056 v1 28 May 1999 Keywords: nonlinear programming, discontinuous derivatives, quantum mechanics, statistics, energy eigenvalues, quantum anharmonic oscillator \$offText Variable ham 'expected value of hamiltonian' alpha 'variational parameter' n 'variational parameter (n = 1: Gaussian trial function)'; Equation hamiltonian; Scalar g / 1 /; hamiltonian.. ham =e= (sqr(n)/2)*(gamma(2 - 1/(2*n))/gamma(1/(2*n)))*(alpha**(1/n)) + (1/2)*(gamma(3/(2*n))/gamma(1/(2*n)))*(alpha**(-1/n)) + g*(gamma(5/(2*n))/gamma(1/(2*n)))*(alpha**(-2/n)); alpha.lo = 0.0001; alpha.up = 10; alpha.l = 1; * gaussian variational method n.fx = 1; Model m / hamiltonian /; solve m minimizing ham using dnlp; Parameter results(*,*); results('Gaussian','Ground') = ham.l; results('Gaussian','alpha') = alpha.l; results('Gaussian','n') = n.l; * post-gaussian variational method n.lo = 0.001; n.up = 10; solve m minimizing ham using dnlp; results('Post-Gaussian','Ground') = ham.l; results('Post-Gaussian','alpha') = alpha.l; results('Post-Gaussian','n') = n.l; option decimals = 6; display results;