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Unformatted text preview: Lecture 13, p 1 But why must I treat the measuring device classically? What will happen to me if I d o n t ??Eugene Wigner There is obviously no such limitation I can measure the energy and look at my watch; then I know both energy and time!L. D. Landau, on the timeenergy uncertainty principle When I hear of Schrdingers cat, I reach for my gun.Stephen W. Hawking Lecture 13, p 2 Lab 3 Comments Lab 3 meets this week if you are normally in 132 Loomis. Lab 3 meets next week if you are normally in 164 Loomis. So does Discussion, and there is a quiz , so dont skip... For the lab: You will need your Active Directory Login See: http://www.ad.uiuc.edu You can save a lot of time by reading the lab ahead of time. Its a tutorial on how to draw wave functions Lecture 13, p 3 Lecture 13: Superposition & TimeDependent Quantum States x  (x,t ) 2 U= U= x L  (x,t=0) 2 U= U= x L Lecture 13, p 4 Last Week Timeindependent Schrodingers Equation (SEQ): It describes a particle that has a definite energy, E . The solutions, (x), are time independent ( stationary states ). We considered two potentials, U(x): Finitedepth square well Boundary conditions. Particle can leak into forbidden region. Comparison with infinitedepth well. Harmonic oscillator Energy levels are equally spaced. A good approximation in many problems. ) ( ) ( ) ( ) ( 2 2 2 2 x E x x U dx x d m = + Lecture 13, p 5 Today Time dependent SEQ: Superposition of states and particle motion Measurement in quantum physics Schrdingers cat Timeenergy uncertainty principle Lecture 13, p 6 TimeDependent SEQ To explore how particle wave functions evolve with time, which is useful for a number of applications as we shall see, we need to consider the timedependent SEQ : Changes from the time independent version: E i d /dt We no longer assume a definite E. (x) (x,t) The solutions will have time dependence. i = (1) appears The solutions will be complex. This equation describes the complete time and space dependence of a quantum particle in a potential U(x). It replaces the classical particle dynamics law, F=ma. The SEQ is linear in , and so the Superposition Principle applies : If 1 and 2 are solutions to the timedependent SEQ, then so is any linear combination of 1 and 2 (example: = 0.6 1 + 0.8 i 2 ) 2 2 2 ( , ) ( , ) ( ) ( , ) 2 d x t d x t U x x t i m dx dt  + = Lecture 13, p 7 Review of Complex Numbers The equation, e i = cos + isin , might be new to you. It is a convenient way to represent complex numbers. It also (once you are used to it) makes trigonometry simpler....
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This note was uploaded on 04/04/2011 for the course PHYSICS 214 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.
 Spring '11
 MESTRE
 Magnetism, Energy

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