# HW2 - Homework#2 Your Name Due on Friday October 14 before...

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Homework #2 Y o u r N a m e : Due on Friday, October 14, before the lecture. Only two problems will be graded explicitly. The last problem is optional. 1) For the problem of a vibrating string attached by two ends, please draw the spacial part of the solution for the third overtone. For this solution, what is the value of n in u n (x,t) ? How many nodes does this solution have? 2) Using the definition for Hermitian operator, determine if the following operators are Hermitian or not. Justify your answer. i. x ii. xd/dx iii. id 2 /dx 2 3) Determine in each of the following cases if the function in the first column is an eigenfunction of the operator in the second column. If so, what is the eigenvalue? i. x 3 d 3 /dx 3 ii. xy ) ( ) ( y y x x iii. Sin Cos 2 2 4) Operate with (i) z y x and (ii) z y x 2 2 2 2 2 on the function z ik y ik x ik e e Ae 3 2 1 . Is the function an eigenfunction of either operator? If so, what is the eigenvalue?

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HW2 - Homework#2 Your Name Due on Friday October 14 before...

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