Construction of a Convergent Perturbation Theory: Case Study of the Anharmonic Oscillator Ground State Energy

1997 ◽  
Vol 66 (12) ◽  
pp. 3693-3695 ◽  
Author(s):  
Biswanath Rath
Keyword(s):  
Perturbation Theory ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Anharmonic Oscillator

REMARKS ON THE GROUND STATE ENERGY OF THE SPIN-BOSON MODEL: AN APPLICATION OF THE WIGNER–WEISSKOPF MODEL

2001 ◽  
Vol 13 (02) ◽  
pp. 221-251 ◽  
Author(s):  
MASAO HIROKAWA
Keyword(s):  
Perturbation Theory ◽  
Spectral Analysis ◽  
Ground State Energy ◽  
Ground State ◽  
Spectral Properties ◽  
State Energy ◽  
Regularity Condition ◽  
Infrared Singularity ◽  
Regular Perturbation ◽  
Boson Model

For the ground state energy of the spin-boson (SB) model, we give a new upper bound in the case with infrared singularity condition (i.e. without infrared cutoff), and a new lower bound in the case of massless bosons with infrared regularity condition. We first investigate spectral properties of the Wigner–Weisskopf (WW) model, and apply them to SB model to achieve our purpose. Then, as an extra result of the spectral analysis for WW model, we show that a non-perturbative ground state appears, and its ground state energy is so low that we cannot conjecture it by using the regular perturbation theory.

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.

GROUND STATE PERTURBATION OF N-ANYON IN A MAGNETIC FIELD

1993 ◽  
Vol 08 (04) ◽  
pp. 341-348 ◽  
Author(s):  
YUN SOO MYUNG ◽  
J.M. CHOI ◽  
M.J. UM ◽  
C. JUE
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Ground State Energy ◽  
Ground State ◽  
Uniform Magnetic Field ◽  
State Energy ◽  
Energy Shift ◽  
Landau Levels ◽  
Fractional Statistics ◽  
First Order

We study N-anyon of the α-statistics in a uniform magnetic field, to investigate certain properties of the ground state of a fractional statistics. Using the improved bosonic end-perturbation theory, we obtain the first order perturbative energy shift of the ground state energy. It is realized that there exists a second order perturbative energy with Landau levels.

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