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Unformatted text preview: EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:1 Neils Bohr Institute, Copenhagen EEE 434/591—Quantum Mechanics David K. Ferry Regents’ Professor Arizona State University EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:2 Schrödinger went to Copenhagen, as did all the early pioneers, to discuss his approach with Bohr. Bohr tried to convince him to change his views, but did not succeed, although the arguments made Schrödinger physically sick. In the end, Schrödinger made the following statement about his thoughts on the Copenhagen interpretation: “If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.” EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:3 EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:4 EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:5 So, in spite of Bohr’s efforts to coerce Schrödinger to renounce his wave picture, modern experiments show us the correctness of the wave approach. Indeed, the “particle” is only a localized wave packet, which appears to us as a localized particle . It is when we transition to the classical world that the particle takes on a life of its own. So, let us return to looking at some simple examples of solving the Schrödinger equation and continue to gain some insight into its workings. EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:6 The Schrödinger Equation: We continue with some Examples We will examine now a single quantum well, but one with a noninfinite depth. x x = 0 V → V 0 x = a x =  a EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:7 IN THE BARRIER REGIONS, WE HAVE TO ASK WHETHER E>V OR E<V. WE FIRST TREAT THE CASE FOR E<V . For the region x > a: Decaying wave moving in +x direction. This must be the wave for x > a . Wave going in –x direction! This must be the wave for x <  a . EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:8 Propagation in the Presence of Two Barriers • The Schrödinger equation takes a SIMILAR form in the barrier and free regions * With some important SUBTLE differences REGION 1: FREE ELECTRON PROPAGATION REGION 2: PROPAGATION IN THE BARRIER REGIONs EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L5:9 Propagation in the Presence of Two Barriers • Since the electron moves CONTINUOUSLY from region 1 to region 2 * We must MATCH the wavefunction solutions Ψ 1 & Ψ 2 ensure continuity * The first thing we note is that there can only be...
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 Fall '08
 ROEDEL
 Schrodinger

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