Wave Function - MasteringPhysics: Assignment Print View...

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[ Print View ] Physics 228 Spring 2008 Wave Function and Schroedinger Equation Due at 11:59pm on Wednesday, April 2, 2008 View Grading Details Finding Probabilities from the Wave Function Learning Goal: To use the wave function for a particle in a box to calculate the probability that the particle is found in various regions within the box. The quantum mechanical probability that a particle described by the (normalized) wave function is found in the region between and is . The specific example of a particle trapped in an infinitely deep potential well, sometimes called a particle in a box, serves as good practice for calculating these probabilities, because the wave functions for this situation are easy to write down. If the ends of the box are at and , then the allowed wave functions are where is the ground-state wave function, is the first excited state, etc. Here are a few integrals that may prove useful: z , z , z , and z . Part A Page 1 of 8 MasteringPhysics: Assignment Print View 5/8/2008 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1116520
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If the particle in the box is in the second excited state (i.e., ), what is the probability that it is between and ? To find this probability, you will need to evaluate the integral . Express your answer as a number between 0 and 1 to three significant figures. ANSWER: = 0.667 Part B If the particle is in the first excited state, what is the probability that it is between and ? Express your answer as a number between 0 and 1 to three signifcant figures. Hint B.1 How to set up the integral Hint not displayed ANSWER: = 0.129 Part C If the particle is in the ground state, what is the probability that it is in a window wide with its midpoint at ? You should be able to answer this part without evaluating any integrals! Since is so small, you can assume that remains constant over that interval, so the integral is approximately . Express your answer as a number between 0 and 1 to three significant figures. ANSWER: = 2.62×10 4 Part D Assume a window as in Part C. Compared to a particle in the ground state, which of the following statements is true for a particle in the first excited state? Hint D.1 How to approach the problem Hint not displayed Page 2 of 8 MasteringPhysics: Assignment Print View 5/8/2008 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1116520
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ANSWER: A particle in the first excited state is more likely to be found in the window . A particle in the first excited state is less likely to be found in the window . A particle in the first excited state is equally likely to be found in the window . Schrödinger Equation and the Particle in a Box
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This note was uploaded on 11/25/2010 for the course PHYSICS 228 taught by Professor Staff during the Spring '08 term at Rutgers.

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Wave Function - MasteringPhysics: Assignment Print View...

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