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

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

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

Path representations of the quantum-mechanical energy-level density

1968 ◽  
Vol 64 (3) ◽  
pp. 787-794 ◽  
Author(s):  
Viktor Bezák
Keyword(s):  
Energy Level ◽  
Mechanical Energy ◽  
Level Density ◽  
Energy Levels ◽  
Partial Sums ◽  
Quantum Mechanical ◽  
Different Types ◽  
Square Well ◽  
The One ◽  
Quantum Mechanical Energy

AbstractThe quantum-mechanical energy-level density g(E) is given as a functional of the quantum-mechanical kernel K(q″, q′, t″ −t′). On taking the kernel K in the Feynman's form, one obtains the function g(E), without solving a Schrödinger equation. As an example, the embedding of a particle in the one-dimensional square well with infinitely high walls is analysed. The functions K(x″, x′, t−t′) and g(E) are represented as sums of terms corresponding to classical paths of different types. By an adequate choice of some terms due to the ‘most important’ paths, one may construct partial sums giving approximations of the function g(E). The utilization of such approximations for estimation of energy levels is demonstrated.

scholarly journals Quantum harmonic free energies for biomolecules and nanomaterials

2022 ◽  
Author(s):  
Alec White ◽  
Chenghan Li ◽  
Garnet Kin-Lic Chan
Keyword(s):  
Mechanical Energy ◽  
System Size ◽  
Quantum Mechanical ◽  
Thermodynamic Quantities ◽  
Free Energies ◽  
Energy Functions ◽  
Molecular Systems ◽  
Large Molecules ◽  
Large Systems ◽  
Quantum Mechanical Energy

Abstract Obtaining the free energy of large molecules from quantum mechanical energy functions is a longstanding challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the thermodynamics of molecular systems of unprecedented size, with modest cost. Using this approach, we compute the vibrational thermodynamics of a series of diamond nanocrystals, and show that the error per atom decreases with system size in the limit of large systems. We further show that we can obtain the vibrational contributions to the binding free energies of prototypical protein-ligand complexes where the exact computation is too expensive to be practical. Our work raises the possibility of routine quantum mechanical estimates of thermodynamic quantities in complex systems.

Sign in / Sign up

Export Citation Format

Share Document