HW05 & Solutions

# HW05 & Solutions - ECE 306 Homework Set#5 Spring...

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ECE 306 Homework Set #5 Spring 2005 (Due 12 noon, Wednesday, March 2, 2005) 1. A beam of non-interacting electrons propagates along the x-axis in an infinite, one-dimensional space with V(x) = 0. a. Many measurements of linear momentum and total energy are made. In 25% of the measurements an electron is found moving to the right with energy E 1 , and in 75% of the measurements an electron is found moving to the left with energy E 2 . Construct a non-normalized wave function for the electron beam, Ψ (x, t) in terms of E 1 , E 2 and fundamental constants, that will account for the stated results. b. Is Ψ (x, t) an eigen function of p x and/or H? c. Does Ψ (x, t) satisfy the time-independent Schroedinger’s equation, energy eigen- value equation, both equations or neither. Explain. d. What is the wave function of an electron after a measurement of its energy yields the result E 2 . 2. A particle of mass m, traveling along the x-axis in a region of constant potential energy has the following wave function: h h / / ) ( 2 2 0 ) , ( iEt V E m ix e e t x

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• Spring '05
• TANG
• Gate, Fundamental physics concepts, wave function, eigen function

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