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dnvlgm
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Can anybody tell me what they mean by 2, 3, 6 or any band hamiltonians. What does it even mean?
How do you get to neglect the electron-hole interaction when you are dealing with an exciton?dnvlgm said:So for instance i have an excitonic state in piece of semiconductor. It occurs to me that the total wavefunction Y would be the product of the individual wavefunctions of the electron and the hole, or
Y_{exciton}=y_{electron}*y_{hole}
Gokul43201 said:You lost me hereow do you get to neglect the electron-hole interaction when you are dealing with an exciton?
How do you get the physics of a bound state if you neglect the interaction? Even in a Wannier-Mott exciton, the binding energy is typically ~100meV. What do you figure is the KE of a free electron or hole at room temperature in your material?dnvlgm said:You do realize this is a Wannier-Mott exciton we are talking about, right? If you look at a later post I mentioned the rod's length is 300amstrong which means it is delocalized and we can neglect the coulomb interaction, for its Bohr radius is way larger than the lattice constant
Gokul43201 said:How do you get the physics of a bound state if you neglect the interaction? Even in a Wannier-Mott exciton, the binding energy is typically ~100meV. What do you figure is the KE of a free electron or hole at room temperature in your material?
Gokul43201 said:What exactly is it you want to achieve? That is not particularly clear. What are you trying to calculate?
A 2-band Hamiltonian is a mathematical model used in quantum mechanics to describe the energy levels and behavior of a system with two energy bands. It takes into account the interactions between particles and the external potential energy.
A 3-band Hamiltonian is a more complex version of a 2-band Hamiltonian that includes a third energy band. This additional band allows for a more accurate description of the system's behavior, particularly in cases where the two bands may overlap.
A 6-band Hamiltonian is a further extension of the 3-band Hamiltonian, including a total of six energy bands. This type of Hamiltonian is often used in more complex systems, such as semiconductors, to accurately describe the interactions between electrons and holes in the material.
The Hamiltonian is a fundamental concept in quantum mechanics that allows scientists to accurately describe the energy levels and behavior of a system. It is used to calculate the time evolution of a quantum system and is essential in understanding the dynamics of particles and their interactions.
The bands in a Hamiltonian are determined by the energy levels of the particles in the system and the external potential energy. The mathematical equations used to describe the interactions between particles and their energy levels are based on principles of quantum mechanics and are solved to determine the bands in the Hamiltonian.