{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

P-Chem II Course HWK 4 solutions

# P-Chem II Course HWK 4 solutions - Phys—Chem...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Phys—Chem. ll [CHM4411—02], Spring 2012 (Distributed/posted on 2/17/11, due on Wed. 2/22/2011) Homework 4 You name: ------ Problem 7.10 M 1 A particle is in a state described by the wavefunction, (/1 = (420% 6"”, where a is constant and x obeys: OSXSW. 1) is w normalized? 2) Determine the expectation value of the commutator of the position and momentum operators: [X, Px]. Exercise 7.1.73 Determine the commutators of the operators: (a) fl— and —1~ dx X \ , .ﬂ Q“, 4 V K 5 mm M Exercise 7.1 7(b) Determine the commutators of the operators A and A: where the5e operators are defined as: 2+m 2—m A=—-—and A+: J5 J5 gr Exercise 7.24 To the movement of a particle in one dimension x (x varies between ~00 and +00) we associate ~0X2 three wavefunctions: (a) 1/1 = 8”“; (b) (/1 : cos(kx); (c) {/2 z e . . . . A h d g; Find out which one of these IS an eigenfunction of the momentum operator, : ~77. I x w. ngQECalculate the average linear momentum of the particle for the wavefunctions (b) and (c) above. M .7 A” W \$2.: .23 Exercise 8.2 Write the Schrodinger equation for a particie moving in 1 dimension potential well of width L (La, box of length L) and express the corresponding normalized wavefunction as function of an integer number n. Can n take any value? (1) Calculate the probability that the particle will be found between 0 and 0.01L in a box of length L when it has: (a) n21, (b) n=2, (c) n=4 (2) Calculate the probability that the particle will be found between 0.65L and 0.67L in a box of length L when it has: (3) n=1, (b) n=2, (c) n=4 Hint: Consider the wavefunction to be constant over these narrow windows. ...
View Full Document

{[ snackBarMessage ]}