It is explained that Braggs reflection causes standing wave patterns at the Brillouin zone boundaries and quantum confinement effect allows the electron to take only the distcrete values of K(wave number). Please give a clear explanation for this statement.
Thanking You.
I really do not understand your quantum confinement. Electron on the 1st Bohr orbit of Hydrogen atom is also quantum confined as much as hydrogen molecule or alpha particle. What you are talking about is known as Bloch theorem http://www.binghamton.edu/physics/docs/note-energy-band.pdf nothing mysterious in this theorem and it is NOT intrisic for quantum mechanics.In mathematics this is known as FLOQUET THEORY https://en.wikipedia.org/wiki/Floquet_theory and has widespread uses elsewhere too
Thank you for responding sir,
I would like to elaborate my question again. Please give me explanation regarding the statement "for a bounded electron quantum confinement of electron allows only specific values of momentum(k or P) hence only corresponding Energy values for specific k values are permitted".
I look forward for an intuitive explanation for Energy Gap formation in band diagram of any material relating its momentum and how confinement is the reason for it.
This statement is confusing. Bounded states are indexed usually with quantum numbers different from k. You'll be safe to number them 1, 2, 3 and so on. Till the delocalized states begin. They can be indexed with k. For example, in the hydrogen atom it is the principle quantum number for the bounded state, and, naturally an electron passing by has a momentum.
Please talk about it at crystal level(i,e electron moving in a crystal with wave Constant K) instead of atom level quantum states.
Does not matter. You terminology is wrong. Bounded states are bounded. They cannot be assigned a wave vector as a quantum number. In solids they are, for example, states of impurities. For bands see Bloch theorem. Extended states can have k. Interaction between bounded states expands their levels into bands. With any k.
Ok Sir,
I am new to this subject, may be my terminology is wrong please tell me if energy gap for any crystalline material is related to quantum confinement effect or not. If yes how is it related. If no, please mention how electrons are restricted to occupy some energy levels calling them as forbidden energy values.
In many online materials they are explaining that ,at the boundaries of brillouins zone electron gets diffracted and hence superposition of electron waves results in standing waves and that is cause for energy gap. But the fact is perfect periodic crystal lattice does not exists there may be probability that standing waves gets superimposed constructively and occupy different energy values.
Even If this content is wrong please let me know how exactly it happens.
No, it is multiple scattering and interference.
The imperfections produce confinement but these levels are not in the band. They are in the gap. They are discrete and one cannot assign any k to them.
Why we cannot any K to them? On what basis they have come to that conclusion.
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