- #1
UbikPkd
- 9
- 0
[tex]\Psi_{n}(x)[/tex] = [tex]\sqrt{2/L}[/tex]sin([tex]\pi[/tex]nx/L), 0 [tex]\leq[/tex]x [tex]\leq[/tex] L
[tex]\Psi_{n}(x)[/tex] = 0, x<0, x>L
[tex]\pi[/tex] is meant to be just normal, not superscript, sorry
n is an integer
show that <[tex]\hat{x}[/tex]> = L/2
<[tex]\hat{x}[/tex]> is the expectation value of the positional operator [tex]\hat{x}[/tex] right?
[tex]\hat{x}[/tex] [tex]\Psi[/tex]= x [tex]\Psi[/tex] i think so...
[tex]\int[/tex]2x/L sin [tex]^{2}[/tex]([tex]\pi[/tex]2nx/L) dx
which gets me L/2 - L[tex]^{2}[/tex]/4n[tex]^{2}[/tex] [tex]\pi[/tex][tex]^{2}[/tex]
but it is supposed to be just L/2 sigh...
any help will be much appreciated
[tex]\Psi_{n}(x)[/tex] = 0, x<0, x>L
[tex]\pi[/tex] is meant to be just normal, not superscript, sorry
n is an integer
show that <[tex]\hat{x}[/tex]> = L/2
<[tex]\hat{x}[/tex]> is the expectation value of the positional operator [tex]\hat{x}[/tex] right?
[tex]\hat{x}[/tex] [tex]\Psi[/tex]= x [tex]\Psi[/tex] i think so...
[tex]\int[/tex]2x/L sin [tex]^{2}[/tex]([tex]\pi[/tex]2nx/L) dx
which gets me L/2 - L[tex]^{2}[/tex]/4n[tex]^{2}[/tex] [tex]\pi[/tex][tex]^{2}[/tex]
but it is supposed to be just L/2 sigh...
any help will be much appreciated