quantum.gms : An application from quantum mechanics
An application from quantum mechanics:
Find energy eigenvalues of the anharmonic oscillator with g=1
in the Gaussian and Post-Gaussian variational methods.
Reference:
- 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
Small Model of Type: DNLP
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$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
$offtext
variables
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;
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