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NNSE508_EM-L8-QM-SSP

NNSE508_EM-L8-QM-SSP - NNSE 508 EM Lecture#8 1 Lecture...

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Unformatted text preview: NNSE 508 EM Lecture #8 1 Lecture contents • A few concepts from Quantum Mechanics • Solid state physics review – Approximations NNSE 508 EM Lecture #8 2 Few concepts from Quantum Mechanics • Psi-function ( , ) • Schrödinger equation • Hamiltonian ) , ( ˆ ) , ( t r H t t r i General Schrödinger equation: If Ĥ does not depend on time ) ( ) ( ) ( 2 ) ( ˆ 2 r E r r V m r H E e r t r w p Et i . . ; ) ( ) , ( Time-independent Schrödinger equation: ) ( ) ( ˆ r E r H Uncertainty principle (Fourier theorem+ w.-p. dualism) p x h NNSE 508 EM Lecture #8 3 Quantum Mechanics: particle in a single-dimensional well ) ( ) ( ) ( ) ( 2 2 2 2 x E x x V dx x d m 0 L V V(x) x No states Localized states (discrete spectrum ) Delocalized states (continuous spectrum ) V(x)=V for x < 0 V(x)=0 for 0 ≤ x ≤ L V(x)=V for x > L L nx L n sin 2 2 2 2 2 2 2 2 2 n mL m k E L n k n n n For infinite barrier, V ∞ NNSE 508 EM Lecture #8 4 Two wells First approximation of perturbation theory : What will happen if the wells are resonant ? What will happen if the wells are resonant ?...
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NNSE508_EM-L8-QM-SSP - NNSE 508 EM Lecture#8 1 Lecture...

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