On classical and quantum harmonic potentials

2000 ◽  
Vol 78 (10) ◽  
pp. 937-946 ◽  
Author(s):  
P Mohazzabi
Keyword(s):  
Potential Energy ◽  
Harmonic Oscillator ◽  
Energy Function ◽  
Mechanical Energy ◽  
Energy Levels ◽  
Potential Energy Function ◽  
Quantum Mechanical ◽  
Quantum Mechanical Energy

To date, the only potential energy function that has been demonstrated to be classical harmonic but not quantum harmonic is that of the asymmetrically matched harmonic oscillator. By investigating the accurate quantum mechanical energy levels of the potential V = V0 [Formula: see text], we demonstrate that this is the second member of the class. PACS No.: 03.65Ge

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

scholarly journals The effects of charge on the potential energy function and energy levels for Cu2n±(n=0,1,2)

2004 ◽  
Vol 53 (1) ◽  
pp. 37
Author(s):  
Mao Hua-Ping ◽  
Wang Hong-Yan ◽  
Tang Yong-Jian ◽  
Zhu Zheng-He ◽  
Zheng Sao-Tao
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Energy Levels ◽  
Potential Energy Function

V.—The Mathematical Representation of the Energy Levels of the Secondary Spectrum of Hydrogen.—II.

1936 ◽  
Vol 55 ◽  
pp. 49-61 ◽  
Author(s):  
Ian Sandeman
Keyword(s):  
Quantum Mechanics ◽  
Potential Energy ◽  
Energy Function ◽  
Hydrogen Molecule ◽  
Energy Levels ◽  
Potential Energy Function ◽  
The State ◽  
Mathematical Representation ◽  
Similar Data ◽  
Wave Mechanics

In a recent paper (Sandeman, 1933) the question of the mathematical representation of the energy levels of the hydrogen molecule by methods based on the old mechanics has been considered. In view of the fact that the wave mechanics has supplanted the older theory, the further application of newer methods to this spectrum is desirable. Richardson and Davidson (1929 b, p. 45) worked out the potential energy function U(ξ) (ξ is denned on p. 51) for the state IsσЗpπ3Π on the old quantum mechanics and on the wave mechanics with the following results: U(ξ) = 5·50ξ2(1 – 1·556ξ + 1·58ξ2 – 1·56ξ3) volts on the old quantum mechanics and U(ξ) = 5·71ξ2(1 – 1·55ξ + 1·58ξ2 – 1·59ξ3) volts on the wave mechanics. They also (loc. cit., pp. 30 and 31) gave the U(ξ)'s for the states Isσ2pσ1∑, Isσ2sσ3∑, and IsσЗdπ1Πb, and on p. 45 they gave the formulæ, based on Fues's (1926) results, for transcribing the old quantum mechanics into the wave mechanics series. Richardson and Das (1929, pt. ii) gave similar data for the state IsσЗpσ3∑.

The influence of distant boundaries on quantum mechanical energy levels

1990 ◽  
Vol 58 (8) ◽  
pp. 751-755 ◽  
Author(s):  
G. Barton ◽  
A. J. Bray ◽  
A. J. McKane
Keyword(s):  
Mechanical Energy ◽  
Energy Levels ◽  
Quantum Mechanical ◽  
Quantum Mechanical Energy
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