Phase-integral calculation of the energy levels of a quantal anharmonic oscillator

1981 ◽  
Vol 24 (10) ◽  
pp. 2586-2598 ◽  
Author(s):  
M. Lakshmanan ◽  
F. Karlsson ◽  
P. O. Fröman
Keyword(s):  
Anharmonic Oscillator ◽  
Energy Levels ◽  
Phase Integral

scholarly journals Energy levels of one-dimensional anharmonic oscillator via neural networks

2019 ◽  
Vol 34 (12) ◽  
pp. 1950088 ◽  
Author(s):  
Halil Mutuk
Keyword(s):  
Neural Network ◽  
Field Theory ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
High Accuracy ◽  
Network System ◽  
Quantum Field ◽  
One Dimensional ◽  
Neural Network System ◽  
Good Agreement

In this work, we obtained energy levels of one-dimensional quartic anharmonic oscillator by using neural network system. Quartic anharmonic oscillator is a very important tool in quantum mechanics and also in the quantum field theory. Our results are in good agreement in high accuracy with the reference studies.

A NONLINEAR-OSCILLATOR MODEL FOR STRONG INTERACTION IN MOLECULAR SOLIDS

2006 ◽  
Vol 20 (30) ◽  
pp. 1953-1955 ◽  
Author(s):  
M. A. GRADO-CAFFARO ◽  
M. GRADO-CAFFARO
Keyword(s):  
Classical Limit ◽  
Vibrational Energy ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
Potential Interaction ◽  
Strong Interactions ◽  
Molecular Solids ◽  
One Dimensional ◽  
Vibrational Energy Levels ◽  
Type Potential

A theoretical model based upon a one-dimensional anharmonic oscillator is proposed in order to describe strong interactions in molecular solids. Vibrational energy levels are studied in terms of the associated vibrational quantum number; in particular, classical limit is discussed. Kinetic energy corresponding to a typical collision process is calculated. In addition, Morse-type potential interaction is found to be an approximation to our model.

Further contributions to the energy levels of a perturbed anharmonic oscillator: Application to adiabatic corrections

1988 ◽  
Vol 88 (7) ◽  
pp. 4351-4356 ◽  
Author(s):  
Gisèle Hadinger ◽  
Y. S. Tergiman ◽  
Gerold Hadinger
Keyword(s):  
Anharmonic Oscillator ◽  
Energy Levels

On the energy levels of an isotropic anharmonic oscillator

1980 ◽  
Vol 13 (9) ◽  
pp. L299-L302 ◽  
Author(s):  
M Lakshmanan ◽  
P Kaliappan
Keyword(s):  
Anharmonic Oscillator ◽  
Energy Levels

Rotation of a rigid diatomic dipole molecule in a homogeneous electric field: I. Schrödinger equation. Quantization conditions according to phase-integral method

1994 ◽  
Vol 347 (1682) ◽  
pp. 1-22 ◽  
Keyword(s):  
Field Strength ◽  
Schrödinger Equation ◽  
Electric Field ◽  
Electric Field Strength ◽  
Integral Method ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Base Function ◽  
Dipole Molecule ◽  
Phase Integral

After a brief historical discussion of the energy quantization according to quantum mechanics of the rigid diatomic dipole molecule in a static electric field, the Schrödinger equation for that system is recalled. Previous attempts to obtain the energy levels clearly indicate that there is a need for a reliable method yielding very accurate eigenvalues for all values of the electric field strength. This is accomplished with the aid of new quantization conditions obtained by means of a phase-integral method involving a general phase-integral approximation of arbitrary order generated from an unspecified base function, which is chosen in two different ways such that, when the electric field strength is equal to zero, simple limiting forms of the quantization conditions give the exact values of the energy levels. The two choices of the base function are expected to be appropriate in the cases when the absolute value of the magnetic quantum number m is sufficiently large and sufficiently small respectively. For every value of m at least one of the two base functions should be useful.

Sign in / Sign up

Export Citation Format

Share Document