Quantum Mechanics => Operators

  • Thread starter jonnylane
  • Start date
  • #1
I'm doing some past papers for my QM finals and I've come across a question that is a bit strange. I'm not sure if it's as easy as it sounds.

X and P are one dimensional position and momentum operators, which take the explicit forms of x and -ihd/dx.

i) write down the explicit forms of X^2 and P^2

now then, is this just x^2 and hd^2/dx^2?

im ok on the next few bits, but:

iv) which, if any, of the two functions exp(ikx) and exp(-ax^2) are eigenfunctions of P^2?

my guess is that, since the eigenfunction of P is exp(ikx), its the other one (and the i has disapeared in the squaring process), but how can i prove this?


Im probably just being paranoid, but can someone verify these answers?

thanks
 

Answers and Replies

  • #2
ahrkron
Staff Emeritus
Science Advisor
Gold Member
756
2
Originally posted by jonnylane
now then, is this just x^2 and hd^2/dx^2?

How did you obtain them? that's the important part. I think you're missing a sign on P^2.

iv) which, if any, of the two functions exp(ikx) and exp(-ax^2) are eigenfunctions of P^2?
how can i prove this?

Remember what an eigenfunction is. You need to plug in both functions on P^2, and see if you get a constant times the original function.
 

Suggested for: Quantum Mechanics => Operators

  • Last Post
Replies
5
Views
363
Replies
7
Views
400
Replies
14
Views
271
Replies
1
Views
224
Replies
8
Views
63
  • Last Post
Replies
22
Views
442
  • Last Post
Replies
8
Views
364
Replies
2
Views
574
Top