QUANTIZATION CONDITION FOR HIGHLY EXCITED STATES

1999 ◽  
Vol 14 (19) ◽  
pp. 1237-1242 ◽  
Author(s):  
FRANCISCO M. FERNÁNDEZ ◽  
RAFAEL GUARDIOLA
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Rational Approximation ◽  
Logarithmic Derivative ◽  
Quantization Condition ◽  
Quantum Mechanical ◽  
Anharmonic Oscillators ◽  
One Dimensional ◽  
Simple Quantum ◽  
Mechanical Models

We develop a quantization condition for the excited states of simple quantum-mechanical models. The approach combines perturbation theory for the oscillatory part of the eigenfunction with a rational approximation to the logarithmic derivative of the nodeless part of it. We choose one-dimensional anharmonic oscillators as illustrative examples.

The Riccati–Padé quantization method for one-dimensional quantum-mechanical models

1996 ◽  
Vol 74 (9-10) ◽  
pp. 697-700 ◽  
Author(s):  
Francisco M. Fernández ◽  
R. H. Tipping
Keyword(s):  
Ground State ◽  
Logarithmic Derivative ◽  
Quantum Mechanical ◽  
Quantization Method ◽  
Anharmonic Oscillators ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Continuum States ◽  
Separable Models ◽  
Mechanical Models

We improve on a previously developed method for the calculation of accurate eigenvalues and eigenfunctions of separable models in quantum mechanics. It consists of the approximation of the logarithmic derivative of the eigenfunction by means of a rational function or Padé approximant. Here we modify the approach by the separation of the function just mentioned into its odd and even parts, thus making the procedure more efficient for treating asymmetric one-dimensional potentials. We obtain the ground-state eigenvalue of anharmonic oscillators with one and two wells and the lowest resonances of anharmonic oscillators that support only continuum states.

scholarly journals A NEW ALGEBRAIC APPROACH TO PERTURBATION THEORY

2005 ◽  
Vol 20 (22) ◽  
pp. 1683-1694 ◽  
Author(s):  
B. GÖNÜL ◽  
N. ÇELİK ◽  
E. OLĞAR
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Large Range ◽  
Algebraic Approach ◽  
Coupling Constant ◽  
Anharmonic Oscillators ◽  
Analytical Treatment ◽  
Exactly Solvable ◽  
Recursion Formulas ◽  
Range Of Values

An algebraic nonperturbative approach is proposed for the analytical treatment of Schrödinger equations with a potential that can be expressed in terms of an exactly solvable piece with an additional potential. Avoiding disadvantages of standard approaches, new handy recursion formulas with the same simple form both for ground and excited states have been obtained. As an illustration the procedure, well adapted to the use of computer algebra, is successfully applied to quartic anharmonic oscillators by means of very simple algebraic manipulations. The trend of the exact values of the energies is rather well reproduced for a large range of values of the coupling constant (g = 0.001–10000).

scholarly journals Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states

2020 ◽  
Vol 153 (20) ◽  
pp. 201103
Author(s):  
Yoshifumi Noguchi ◽  
Miyabi Hiyama ◽  
Motoyuki Shiga ◽  
Hidefumi Akiyama ◽  
Osamu Sugino
Keyword(s):  
Excited States ◽  
State Of The Art ◽  
Critical Role ◽  
Quantum Mechanical ◽  
The Stability

Low-Lying Excited States of C120 and C151: A Multireference Perturbation Theory Study

2010 ◽  
Vol 114 (47) ◽  
pp. 12363-12368 ◽  
Author(s):  
Tetsuya Sakata ◽  
Yukio Kawashima ◽  
Haruyuki Nakano
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Multireference Perturbation Theory
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