Hamiltonian for a dimer approaching a surface

In summary, the conversation is about a problem involving deriving a Hamiltonian for a system. The speaker is unsure of how to approach the problem and is looking for suggestions or guidance. The problem involves polar and azimuthal terms canceling out and the model assumes a fixed angle between the surface and the dimer, neglecting angular momentum. The kinetic energy term can be derived from two parallel masses and separating out center of mass and relative coordinates.
  • #1
AllenFaust
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Hi! it's been a day since I have started this problem. I was wondering how I could arrive to this Hamiltonian?
And I'm a bit at a lost on how exactly to derive this? I hope anyone can help me with this, even a suggestion of good starting point would be much appreciated.

upload_2017-6-9_18-1-7.png


Basically the problem is to derive a hamiltonian for the system here.
upload_2017-6-9_18-2-6.png


Regarding this, I'm currently thinking of having a set of polar and azimuthal terms cancel out and thus leading to this maybe?

Thank you very much!
 

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  • #2
The model appears to assume that the angle between the surface and the dimer is fixed, and neglects angular momentum. The kinetic energy term can be derived starting from two masses parallel to the surface, then separating out center of mass and relative coordinates.
 

1. What is the Hamiltonian for a dimer approaching a surface?

The Hamiltonian for a dimer approaching a surface is a mathematical expression that describes the energy of the system, taking into account the positions and interactions of the dimer and the surface. It includes terms for the kinetic energy of the dimer, its potential energy due to interactions with the surface, and any external forces acting on the system.

2. How is the Hamiltonian for a dimer approaching a surface derived?

The Hamiltonian for a dimer approaching a surface is derived using principles of classical mechanics and quantum mechanics. It takes into account the physical properties of the dimer and the surface, such as their masses and charges, and the laws of motion and energy conservation.

3. What factors affect the Hamiltonian for a dimer approaching a surface?

The Hamiltonian for a dimer approaching a surface is affected by various factors, such as the distance between the dimer and the surface, the angle of approach, the properties of the dimer and the surface, and the presence of any external forces or fields. These factors can influence the energy of the system and the dynamics of the dimer-surface interaction.

4. How is the Hamiltonian for a dimer approaching a surface used in research?

The Hamiltonian for a dimer approaching a surface is used in research to study the behavior of molecules or particles near surfaces, which has important applications in fields such as materials science, nanotechnology, and biophysics. It can be used to predict the stability and reactivity of molecular systems on surfaces, and to understand the mechanisms of surface-based reactions and processes.

5. Can the Hamiltonian for a dimer approaching a surface be extended to more complex systems?

Yes, the Hamiltonian for a dimer approaching a surface can be extended to more complex systems, such as multiple dimers or larger molecules, by including additional terms for their interactions and dynamics. It can also be modified to incorporate quantum effects, such as tunneling and quantum confinement, for a more accurate description of the system. However, the complexity of the Hamiltonian increases with the number of particles and interactions, making it more challenging to solve analytically.

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