tailieunhanh - Electronic Materials Part 3

Tham khảo tài liệu 'electronic materials part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Wave-particle Duality Electrons are not just particles Compton Planck Einstein - light xrays can be particle-like DeBroglie - matter can act like it has a wave-nature Schrodinger Born - Unification of wave-particle duality Schrodinger Equation Ề------------------------------------------------------------- . E. Fitzgerald-1999 15 8 DeBroglie Matter is Wave His PhD thesis X h p also for matter To verify need very light matter p small so X is large enough Need small periodic structure on scale of X to see if wave is there diffraction Solution electron diffraction from a crystal NX 2dsin0 For small 0 0 X d so X must be on order of d in order to measure easily E. Fitzgerald-1999 17 9 Quantum Mechanics - Wave Equation Classical Hamiltonian -p- V X y z E 2 m QM Operators E h i d d t - -h A2V V x y z v - d - 2 m i G t 1. V and A V must be finite continuous and single valued. 2. VV real with VV dV probability of finding particle in volume dV. 3. Average or expectation value of variable a Jv a op VdV v . Tuller-2001 19 Time and Spatial Dependence of V Assume V x y z t separable into V x y z and ộ t Applying separation of variables - h 1 2 3 V 2V V - 1 dộ 2m V i Ộ dt constant Time-Dependent Equation Ộ t Ae s h t Ae e ho Time-Independent Equation V 2V 2m g- V v 0 Solutions Vn -eigenfunctions n -eigenvalues ------------------------------------------ . Tuller-2001 20 .