| Topic: |
Science > Physics |
| User: |
"DickRFL" |
| Date: |
02 Feb 2004 07:40:39 PM |
| Object: |
Symmetric, antisymmetric and parity |
I'm an interested layperson trying to obtain a little knowledge about
quantum mechanics so please excuse the poor terminology I use in
posing this question.
Problem 5.5 In David Griffiths "Introduction to Quantum
Mechanics" says: Imagine two non interacting particles, each of mass
m, in the infinite square well. If one is in the state psi_n and the other
in
state psi_m orthogonal to psi_n, calculate <(x_1 - x_2)^2 >,
assuming that (a) they are distinguishable particles, (b) they
are identical bosons, (c) they are identical fermions.
I get the following answers:
(a) a^2 [1/6 - 1/(2*pi^2)(1/n^2 + 1/m^2)
(b) The answer to (a) minus (128*a^2*m^2n^2) / (pi^4(m^2 - n^2))^4
But this last term is present only when m,n have opposite parity.
(c) The answer to (a) *plus* the term in (b) with the same stipulation as in
(b)
What does this mean? It seams to be saying that all three particles would
have the same separation unless their states have opposite parity. Is this
correct? Why would that be true? Thanks
.
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