Lecture 04

Lecture 04 - EEE 434/591Quantum Mechanics L4:1 David K....

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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L4:1 EEE 434/591—Quantum Mechanics David K. Ferry Regents’ Professor Arizona State University Arosa, Switzerland
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L4:2 The Schrödinger Equation: Herman Weyl described Schrödinger’s success with the wave equation as: “…a late erotic outburst…” It turns out that Schrödinger was on Christmas vacation with a girlfriend in Arosa, Switzerland, when he developed the wave equation and wrote his 4 key papers, also showing the equivalence to matrix mechanics and solving the atomic structure and developing perturbation theory. Now, last time we talked about entanglement and delayed choice. Schrödinger brought this to us via his famous cat!
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L4:3
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L4:4 Before measurements…., the cat is both alive and dead—there exists no reality of either state until it is measured. This is the essence of the Copenhagen Interpretation. Before we measure, there are only potentialities , not real things. The argument made by Einstein is for the existence of a conceptual reality before measurement. It is this existence of a reality before measurement, which is really at the heart of the EPR assertions. And this is the heart of the argument. Now, the result from this is that both potential states are represented in the entangled wave function, which collapses under measurement to the one outcome. This collapse occurs over vast distances without regard to the speed of light! This was unacceptable to Einstein, and Schrödinger wasn’t a fan either. But, this extensive nonlocality and entanglement have been demonstrated experimentally, at least to the satisfaction of many observers.
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L4:5
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L4:6 * By performing the SEPARATION OF VARIABLES * Equation 1 is the time INDEPENDENT Schrödinger equation * Equation 2 is the energy eigenfunction temporal equation * In these equations the constant E represents the TOTAL ENERGY Of the particular particle under study From the first equation, we see why the Hamiltonian H= T+V is often called the “energy operator.” Let’s now turn our attention to what the Schrödinger equation can tell us.
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EEE 434 Quantum Mechanics http://www.eas.asu.edu/~ferry/EEE434.htm L4:7 The Schrödinger Equation * Consider a particle of mass m that moves FREELY in one dimension * The energy of the electron is stored completely as KINETIC ENERGY * Solution of the Schrödinger equations thus proceeds as follows ∴ Ψ ( x , t ) = A exp ikx ( ) + B exp ikx ( ) [ ] e i ω t THE TEMPORAL EQUATION TIME DEPENDENT EQUATION This is a tautology : we started with the assumption that the electron was a wave, now we have solved to show that it is a wave…. .
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Lecture 04 - EEE 434/591Quantum Mechanics L4:1 David K....

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