ขอต้อนรับ ผู้มาเยือน กรุณา ล็อกอิน หรือ สมัครสมาชิก

ล็อกอินด้วยชื่อผู้ใช้ รหัสผ่่าน และระยะเวลาใช้งาน

 
Advanced search

41359 Posts in 6208 Topics- by 8798 Members - Latest Member: ugkapon
Pages: 1   Go Down
Print
Author Topic: GR8677.057  (Read 3068 times)
0 Members and 1 Guest are viewing this topic.
conantee
SuperHelper
*****
Offline Offline

Posts: 1400

เราเป็นอย่างไร สังคมเป็นอย่างนั้น


« on: January 04, 2010, 04:39:39 AM »

57. Which of the following is an eigenfunction of the linear momentum operator  -i \hbar \frac{\partial}{\partial x} with a positive eigenvalue  \hbar k; i.e., an eigenfunction that describes a particle that is moving in free space in the direction of positive x with a precise value of linear momentum?
(A)  \cos kx
(B)  \sin kx
(C) e^{-ikx}
(D) e^{ikx}
(E) e^{-kx}
Logged
conantee
SuperHelper
*****
Offline Offline

Posts: 1400

เราเป็นอย่างไร สังคมเป็นอย่างนั้น


« Reply #1 on: February 01, 2010, 08:17:15 AM »

Let's remind ourselves what the eigenfunction of an operator Q is...
f is eigenfunction of an operation Q if Qf=cf where c is constant.

In this case, we seek for f s.t. -i \hbar \frac{\partial}{\partial x}f(x) = \hbar k f(x).

Looking at choices we have, (A) and (B) are wrong since their derivatives are not in the form of themselves (derivative of sine is cosine, not sine itself, for example).
(E) is also wrong, since its derivative does not give i to cancel with i next to the derivative.

Now, just try plug (C) and (D) to check which one is a solution. We found that the answer is (D).

The correct answer is (D). 59 of 100 got the correct one.
« Last Edit: September 20, 2010, 09:08:17 PM by conantee » Logged
Pages: 1   Go Up
Print
Jump to: