Ch39 - Chapter 39 More About Matter Waves University at...

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1 Chapter 39 More About Matter Waves 39- University at Buffalo Physics Dept. Sculpture by R. Reitzenstein
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2 Chapter 39 What is Physics? One of the long-standing goals of physics has been to understand the nature of atom. The development of quantum mechanics provided a framework for understanding this and many other mysteries. The basic premise of quantum mechanics is that moving particles (electrons, protons, etc) are best viewed as matter waves whose motions are governed by Schrödinger’s equation. Although this premise is also correct for massive objects (baseballs, cars. Planets, etc.) where classical Newtonian mechanics still predicts behavior correctly, it is more convenient to use classical mechanics in that regime. However, when particle masses are small, quantum mechanics provides the only framework for describing their motion. Before applying quantum mechanics to the atomic structure, we will first explore some simpler situations. Some of these oversimplified examples, which previously were only seen in introductory textbooks, are now realized in real devices developed by the rapidly growing field of nanotechnology. More About Matter Waves 39-
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3 This observation also applies to matter waves. String Waves and Matter Waves 39- Confinement of wave leads to quantization: existence of discrete states with discrete energies. Wave can only have those energies. In Ch. 16 we saw that two kinds of waves can be set up on a stretched string: traveling waves and standing waves. •finite length string (e.g., clamped both ends) standing waves only discrete frequencies or wavelengths confining a wave in a finite region leads to the quantization of its motion with discrete states each defined by a quantized frequency. • atomic electron (e.g., valence): Coulomb attraction to nucleus spatial confinement electron can exist only in discrete states, each with a discrete energy •infinitely long string traveling waves frequency or wavelength can have any value. • electron moving +x-direction and subject to no force (free particle) wavelength ( λ = h/p ), frequency ( f=v/ λ ), and energy ( E=p 2 /2m ) can have any reasonable value
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4 Fig. 16-23 One-Dimensional Trap: Energies of a Trapped Electron 39- , for 1,2,3 2 n Ln λ == () sin , for 2 n n yx A x n ⎛⎞ ⎜⎟ ⎝⎠ n is a quantum number, identifying each state (mode) Fig. 39-1 Fig. 39-2
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5 Finding the Quantized Energies 39- Fig. 39-2 2 = 2 for 0 , 2 pm Km E x L hh p mE λ =< < == Infinitely deep potential well Fig. 39-3 2 2 2 , for 1,2,3 8 n h En n mL ⎛⎞ ⎜⎟ ⎝⎠
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6 Energy Changes 39- Fig. 39-4 high low E EE Δ =− high low hf E E E = Δ= Confined electron can absorb photon only if photon energy hf= Δ E , the energy difference between initial energy level and a higher final energy level.
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Ch39 - Chapter 39 More About Matter Waves University at...

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