Accurate eigenvalues and eigenfunctions for quantum-mechanical anharmonic oscillators

1993 ◽  
Vol 26 (23) ◽  
pp. 7169-7180 ◽  
Author(s):  
F M Fernandez ◽  
R Guardiola
Keyword(s):  
Quantum Mechanical ◽  
Anharmonic Oscillators ◽  
Eigenvalues And Eigenfunctions

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.

Some quantum mechanical solutions in nonrelativistic anti-Snyder framework

2017 ◽  
Vol 32 (27) ◽  
pp. 1750170 ◽  
Author(s):  
Homa Shababi ◽  
Won Sang Chung
Keyword(s):  
Neutron Star ◽  
Harmonic Oscillator ◽  
Free Particle ◽  
Three Dimensions ◽  
One Dimension ◽  
Quantum Mechanical ◽  
Momentum Representation ◽  
Eigenvalues And Eigenfunctions

In this paper, we investigate nonrelativistic anti-Snyder model in momentum representation and obtain quantum mechanical eigenvalues and eigenfunctions. Using this framework, first, in one dimension, we study a particle in a box and the harmonic oscillator problems. Then, for more investigations, in three dimensions, the quantum mechanical eigenvalues and eigenfunctions of a free particle problem and the radius of the neutron star are obtained.

Dirichlet and von Neumann Basis Set for Quantum Mechanical Anharmonic Oscillators

1983 ◽  
Vol 38 (4) ◽  
pp. 473-476 ◽  
Author(s):  
Alejandro M. Mesón ◽  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Variational Method ◽  
Harmonic Oscillator ◽  
Lower Bounds ◽  
Neumann Boundary ◽  
Basis Set ◽  
Basis Sets ◽  
Upper And Lower Bounds ◽  
Quantum Mechanical ◽  
Anharmonic Oscillators ◽  
Von Neumann

It is shown that accurate upper and lower bounds to the eigenvalues of anharmonic oscillators can be obtained by means of the Rayleigh-Ritz variational method and two trigonometric basis sets of functions which satisfy Dirichlet and Von Neumann boundary conditions. Numerical results show that the Dirichlet basis set is more appropriate than the harmonic oscillator one for calculating eigenvalues and the value of eigenfunctions at the origin.

Is there any unique frequency operator for quantum-mechanical anharmonic oscillators

2005 ◽  
Vol 341 (5-6) ◽  
pp. 390-400 ◽  
Author(s):  
Anirban Pathak ◽  
Francisco M. Fernández
Keyword(s):  
Quantum Mechanical ◽  
Anharmonic Oscillators
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