A fast algorithm for the perturbative calculation of the ground-state energy of the quantum-mechanical anharmonic oscillator

1985 ◽  
Vol 43 (7) ◽  
pp. 329-332 ◽  
Author(s):  
P. C. W. Fung ◽  
Wai bong yeung
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Fast Algorithm ◽  
State Energy ◽  
Anharmonic Oscillator ◽  
Quantum Mechanical ◽  
Perturbative Calculation

Degenerate trajectories and Hamiltonian envelopes in the method of self-similar approximations

1993 ◽  
Vol 71 (11-12) ◽  
pp. 537-546 ◽  
Author(s):  
V. I. Yukalov ◽  
E. P. Yukalova
Keyword(s):  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
Approximate Calculation ◽  
State Energy ◽  
Anharmonic Oscillator ◽  
New Techniques ◽  
Self Similar ◽  
Very High

We study two new techniques for the approximate calculation of the eigenvalues of the Schrödinger equation. These techniques are variants of the method of self-similar approximations suggested recently by one of the authors. We illustrate the ideas by an anharmonic oscillator problem. We show that the precision of the method can be very high. For example, the ground-state energy of an anharmonic oscillator can be calculated with an error not exceeding 0.07% for all anharmonicity parameters ranging from zero to infinity.

ALGORITHM FOR CALCULATING FUNCTIONS IN METHOD OF SUCCESSIVE APPROXIMATIONS

1989 ◽  
Vol 03 (11) ◽  
pp. 1691-1702 ◽  
Author(s):  
V.I. YUKALOV
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Anharmonic Oscillator ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Approximate Expressions

A new algorithm is proposed for constructing unknown functions with the help of their several approximate expressions. The algorithm is illustrated by calculating the ground-state energy of anharmonic oscillator. Different variants of the method are analysed, and it is shown that the accuracy of the calculations can be carried to 0.1%.

GROUND STATE PROPERTIES OF THE SIMPLIFIED HUBBARD MODEL

1992 ◽  
Vol 06 (20) ◽  
pp. 1245-1253 ◽  
Author(s):  
PAVOL FARKASOVSKY
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Magnetic State ◽  
Lattice Structure ◽  
Total Spin ◽  
Quantum Mechanical ◽  
Spin Singlet

We present the exact solution of the simplified Hubbard model in which only one kind of electrons can hop and this quantum mechanical hopping of electrons is assumed to be unconstrained. It is shown that the model still behaves non-trivially, although it no longer depends on the lattice structure and the dimensionality of the system. For this case we find: (i) a gap in the ground state energy always exists at the half-filled band point (n = 1), (ii) a preferred magnetic state at n = 1 and large U is a total spin singlet, (iii) U-dependence of the ground state energy has qualitatively the same form as one of the conventional Hubbard model with the (t2/U)-behavior at large U. A phase diagram of the model is discussed.

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