Accurate energy levels and partition function of a quantum-mechanical anharmonic oscillator

1987 ◽  
Vol 36 (4) ◽  
pp. 1273-1275 ◽  
Author(s):  
Anna Okopińska
Keyword(s):  
Partition Function ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
Quantum Mechanical

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.

Semiclassical variational calculation of energy levels of He@C70

2006 ◽  
Vol 84 (2) ◽  
pp. 145-164
Author(s):  
G R Lee-Dadswell ◽  
C G Gray
Keyword(s):  
Variational Methods ◽  
Mechanical Energy ◽  
Energy Levels ◽  
High Accuracy ◽  
Variational Calculation ◽  
Quantum Mechanical ◽  
Simplified Models ◽  
Trial Solution ◽  
Quantum Mechanical Energy ◽  
Very High

Semiclassical variational methods are used to obtain estimates of the quantum mechanical energy levels for two simplified models of the potential seen by a helium atom trapped inside a C70 cage. We find that with the use of a simple trial solution, the calculations are simple. A more complicated trial trajectory, while improving some results of the calculation, makes the calculation prohibitively difficult. We also observe that as long as the precessional frequency of the orbits is small we can obtain very high accuracy in our results. However, the inability to accurately predict precessional frequencies results in poor prediction of energy levels when the precessional frequency is large.PACS No.: 5.45.Mt

A semiclassical correction for quantum mechanical energy levels

2010 ◽  
Vol 133 (5) ◽  
pp. 054101 ◽  
Author(s):  
Alexey L. Kaledin ◽  
C. William McCurdy ◽  
William H. Miller
Keyword(s):  
Mechanical Energy ◽  
Energy Levels ◽  
Quantum Mechanical ◽  
Quantum Mechanical Energy
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