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Instance quantum

Find energy eigenvalues of the anharmonic oscillator with g=1 in the Gaussian and Post-Gaussian variational methods.

Formatsⓘ	ams gms osil
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.80490293 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ
Referencesⓘ	Ogura, Akihiro, Post-Gaussian variational method for quantum anharmonic oscillator, Tech. Rep. arXiv:physics/9905056v1, Laboratory of Physics, College of Science and Technology, Nihon University, 1999.
Sourceⓘ	GAMS Model Library model quantum
Applicationⓘ	Quantum Mechanics
Added to libraryⓘ	18 Aug 2014
Problem typeⓘ	NLP
#Variablesⓘ	2
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	unknown
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	0
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div gamma mul rpower sqr
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	0
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	2.5000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          1        1        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        3        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          3        1        2        0
*
*  Solve m using DNLP minimizing objvar;


Variables  objvar,x2,x3;

Equations  e1;


e1.. -(0.5*sqr(x3)*Gamma(2 - 0.5/x3)/Gamma(0.5/x3)*x2**(1/x3) + 0.5*Gamma(1.5/
     x3)/Gamma(0.5/x3)*x2**(-1/x3) + Gamma(2.5/x3)/Gamma(0.5/x3)*x2**(-2/x3))
      + objvar =E= 0;

* set non-default bounds
x2.lo = 0.0001; x2.up = 10;
x3.lo = 0.001; x3.up = 10;

* set non-default levels
x2.l = 1;
x3.l = 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set DNLP $set DNLP DNLP
Solve m using %DNLP% minimizing objvar;