NNSE618-L2-QM_SSP

NNSE618-L2-QM_SSP - Orbital structure and energy levels of Si atom Orbital structure Energy levels of electrons in silicon 3s 3p Silicon 1s 2 2s 2

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NNSE 517 Fall 2009 Lecture #2 1 Lecture contents Quantum mechanics and solid state physics review Interaction of two wells Many wells: formation of bands
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NNSE 517 Fall 2009 Lecture #2 2 Secondary quantization: photons Velocity c = ln Momentum Photon energy: Energy of optical field (ensemble of harmonic oscillators) n h E l h k p 2     2 1 , , k n k E
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NNSE 517 Fall 2009 Lecture #2 3 Two wells First approximation of perturbation theory: What will happen if the wells are resonant ? 1 2 1 1 2 * 1 | | ) ( V dx x V E  0 L V(x) x V 2 (x) E V 1 (x) E V V T r H ) ( ) ( ˆ 2 1 2 2 1 1 C C Solution in the form: Negative
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NNSE 517 Fall 2009 Lecture #2 4 Two wells: Solution
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NNSE 517 Fall 2009 Lecture #2 5 Two wells: energy level splitting Resonant levels split Splitting increases at small distances E E 0 L 2 1 1 1 2 1 | | | | V V E   2 1 2 1 0 V(x) x Negative
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NNSE 517 Fall 2009 Lecture #2 6
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Unformatted text preview: Orbital structure and energy levels of Si atom Orbital structure Energy levels of electrons in silicon 3s 3p Silicon: 1s 2 2s 2 2p 6 3s 2 3p 2 NNSE 517 Fall 2009 Lecture #2 7 Bonding and antibonding Antibonding Bonding Wave function Probability density function When two atoms brought together, wave functions interact each other and energy levels split. NNSE 517 Fall 2009 Lecture #2 8 Periodic Potential Well • Formation of energy band • Width depends mainly on interaction of the closest neighbors • Wave-functions are renormalized R V(x) x 2 1 1 | | 2 V E NNSE 517 Fall 2009 Lecture #2 9 Energy levels of Si as a function of interatomic spacing Interatomic spacing Attraction Repulsion Close Far 3p 2 3s 2 Potential energy Low High When N Si atoms brought together...
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This note was uploaded on 11/07/2011 for the course NNSE 618 taught by Professor Sergeoktyabrsky during the Spring '11 term at SUNY Albany.

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NNSE618-L2-QM_SSP - Orbital structure and energy levels of Si atom Orbital structure Energy levels of electrons in silicon 3s 3p Silicon 1s 2 2s 2

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