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.

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.

scholarly journals Spectrum of one-dimensional anharmonic oscillators

2005 ◽  
Vol 83 (5) ◽  
pp. 541-550 ◽  
Author(s):  
H A Alhendi ◽  
E I Lashin
Keyword(s):  
Power Series ◽  
Morse Potential ◽  
Power Series Expansion ◽  
High Accuracy ◽  
Inner Product ◽  
Quantization Method ◽  
Anharmonic Oscillators ◽  
Product Quantization ◽  
One Dimensional ◽  
03.65 Ge

We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high accuracy as the values recently obtained for the unbounded case by the inner-product quantization method. We also apply our method to the Morse potential. The eigenvalues obtained in this case are in excellent agreement with the exact values for the unbounded Morse potential. PACS Nos.: 03.65.Ge, 02.30.Hq

scholarly journals SUPERSYMMETRY: A CONSEQUENCE OF SMOOTHNESS?

2002 ◽  
Vol 17 (15) ◽  
pp. 2073-2093
Author(s):  
H. B. NIELSEN ◽  
S. PALLUA ◽  
P. PRESTER
Keyword(s):  
Ground State ◽  
Vacuum Energy ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Ground State Properties ◽  
Mechanical Models ◽  
Supersymmetric Theories

The consequences of certain simple assumptions like smoothness of ground state properties and vanishing of the vacuum energy (at least perturbatively) are explored. It would be interesting from the point of view of building realistic theories to obtain these properties without supersymmetry. Here we show, however, at least in some quantum mechanical models, that these simple assumptions lead to supersymmetric theories.

scholarly journals Models for the BPS Berry connection

2020 ◽  
pp. 2150007
Author(s):  
Satoshi Ohya
Keyword(s):  
Ground State ◽  
Monotonic Function ◽  
Quantum Mechanical ◽  
Model Parameters ◽  
State Sector ◽  
Yang Mills ◽  
Systematic Construction ◽  
Mechanical Models

Motivated by the Nahm’s construction, in this paper, we present a systematic construction of Schrödinger Hamiltonians for a spin-1/2 particle where the Berry connection in the ground-state sector becomes the Bogomolny–Prasad–Sommerfield (BPS) monopole of SU(2) Yang–Mills–Higgs theory. Our construction enjoys a single arbitrary monotonic function, thereby creating infinitely many quantum-mechanical models that simulate the BPS monopole in the space of model parameters.

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