ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The eigenvalue moment method (EMM) has proven to be an effective technique for generating converging lower and upper bounds to the bosonic ground state energy of singular, strongly coupled, quantum systems. Application of EMM theory requires an appropriate linearization of the highly nonlinear Hankel–Hadamard (HH) moment determinant constraints for the (n+1)×(n+1) Hankel matrices Mn[u]≡Mˆn0+∑i=1msMˆniu i), dependent on the missing moment variables {u(i)}≡u. We propose an alternate variational formulation utilizing the functions Det(Mn+1[u])/Det(Mn[u]), which we prove to be locally convex over the missing moment subset satisfying the HH positivity conditions Det(Mν[u])(approximately-greater-than)0, for ν≤n. Additional features of this variational formulation facilitate its application to important problems such as the octic, sextic, and quartic anharmonic oscillators. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531455
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