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Unformatted text preview: “But why must I treat the measuring device classically? What will happen to me if I don’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 Schrödinger’s cat, I reach for my gun.”Stephen W. Hawking Physics Colloquium Physics Colloquium “Spin Based Testbeds for Quantum Information Processing” Professor David G. Cory Massachusetts Institute of Technology Department of Nuclear Science and Engineering February 14, 2008 4:00 pm, Room 141 Loomis Lab Special (Optional) Lecture Special (Optional) Lecture “Quantum Information” z One of the most modern applications of QM z quantum computing z quantum communication – cryptography, teleportation z quantum metrology z PGK will give a special 214level lecture on this topic z Sunday, Feb. 17 z 4 pm, 151 Loomis z Attendance is optional, but encouraged. Superposition & TimeDependent Quantum States ψ (x,t)  2 U= ∞ x U= ∞ x L Overview Overview z Superposition of states and particle motion z ‘Packet States’ in a Box z Measurement in quantum physics z Schrödinger’s Cat z TimeEnergy Uncertainty Principle Time Time independent independent SEQ SEQ z Up to now, we have considered quantum particles in “ stationary states ,” and have ignored their time dependence Remember that these special states were associated with a single energy (from solution to the SEQ) “eigenstates” ) ( ) ( ) ( ) ( 2 2 2 2 x E x x U dx x d m ψ ψ ψ = + − = U= ∞ ψ (x) L U= ∞ n=1 n=2 x n=3 “Functions that fit”: ( λ = 2L/n) ψ (x) L x “Doesn’t fit”: Review Review Complex Numbers The equation, e i θ = cos θ + isin θ , 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. a) Draw an Argand diagram of e i θ . b) Suppose that θ varies with time, θ = ω t . How does the Argand diagram behave? Solution: a) b) a) The Argand diagram of a complex number, A , puts Re(A) on the xaxis and Im(A) on the y axis. Notice the trig relation between the x and y components. θ is the angle of A from the real axis. In an Argand diagram, e i θ looks like a vector of length 1, and components (cos θ , sin θ ) . b) At t = 0 , θ = 0 , so A = 1 (no imaginary component). As time progresses, A rotates counterclockwise with angular frequency ω . Re(A) Im(A) θ A = e i θ Re(A) Im(A) θ = ω t A = e i ω t t = 0 ce i θ ( c and θ both real), is a complex number of magnitude, c . The magnitude of a complex number, A , is A = √ (A*A) , where A* is the complex conjugate of A : Im(A*) = Im(A). Lecture 9, Act i Lecture 9, Act i We know that 1. What is (i)i?...
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This note was uploaded on 09/12/2009 for the course PHYS 214 taught by Professor Debevec during the Spring '07 term at University of Illinois at Urbana–Champaign.
 Spring '07
 Debevec
 Energy

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