3890ps3_09 - Chem 3890 Physical Chemistry I Fall 2009...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chem 3890 Physical Chemistry I Fall 2009 Chemistry 3890 Problem Set 3 Fall 2009 Due: in class, Friday, September 25 Last revised: September 20, 2009 Additions/corrections: Reminder : To clear global variables, use Remove["Global ` * "] Problem 1 Define a wavefunction ( x ) = A e ikx e- ( x- x ) 2 / 2 (1) where k and x are real, and A is a (real) normalization constant. 1. Calculate the normalization constant A for general ( k,x ). Use the normalized for the rest of the problem. 2. Calculate ( x ) , ( x 2 ) and x for general ( k,x ). Do your answers depend on k ? 3. Calculate ( p ) , ( p 2 ) and p for general ( k,x ). (Do not use the numerical value for planckover2pi1 ; keep your answer in symbolic form.) 4. Calculate the uncertainty product x p for general ( k,x ). Does your expression depend on the parameters k or x ? As you can see, the wavefunctions ( x ) are very useful in that the mean (expectation) values of position and momentum can be dialled in through the choice of parameters x and k . Consider two normalized wavefunctions a ( x ) and b ( x ) of the form (1), having ( x ) = 2, ( p ) = 0 ( a ( x )) and ( x ) = 2, ( p ) = 4 planckover2pi1 ( b ( x )), respectively. 5. Make plots of the real part (Re[ ]), the imaginary part (Im[ ]), and the associated probability density ( x ) for each state. Is there any way that the states a and b can be distinguished on the basis of expectation values of functions of the position variable x (for example, evaluation of higher moments ( x n ) )? If yes, explain how; if no, explain why....
View Full Document

This note was uploaded on 08/25/2011 for the course CHEM 3890 at Cornell University (Engineering School).

Page1 / 3

3890ps3_09 - Chem 3890 Physical Chemistry I Fall 2009...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online