Message Boards Message Boards

0
|
4505 Views
|
2 Replies
|
3 Total Likes
View groups...
Share
Share this post:

Heisenberg uncertainty for the harmonic oscillator?

Posted 5 years ago

I have to do a program about the Heisenberg uncertainty for the harmonic oscillator. I wrote all the integrals that I need to use for the medium values and the specific function of the oscillator, but it doesn't work...Could someone help me please?

?[n_, x_] := Sqrt[?/(2^n n!  Sqrt[?])] HermiteH[n, ? x ] E^(-((? x)^2/2)) /. ? -> 1;

mediex[i_, x_] := \!\(\*SubsuperscriptBox[\(?\), \(0\), \(?\)]\(\((Abs[\?[i, x]])\)^2*x \[DifferentialD]x\)\)
mediex[5, x]

15/(8 Sqrt[?])

mediex2[i_, x_] := \!\(\*SubsuperscriptBox[\(?\), \(0\), \(?\)]\(\((Abs[\?[i, x]])\)^2*x^2 \[DifferentialD]x\)\)

mediex2[5, x]

11/4

mediep[i_, x_] := \!\(\*SubsuperscriptBox[\(?\), \(0\), \(?\)]\(?[i, x]*\((\(-i?\)\ )\) D[?[i, x], 
    x] \[DifferentialD]x\)\)

mediep[5, x]

0

mediep2[i_, x_] := \!\(\*SubsuperscriptBox[\(?\), \(0\), \(?\)]\(?[i, x]*\((?^2\ )\) D[D[?[i, x], x], 
    x] \[DifferentialD]x\)\)

mediep2[5, x]

-((11 ?^2)/4)

POSTED BY: Ana Monea
2 Replies

I am by no means sure, but I think you should write

mediep2[i_, x_] := -\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\(\[Psi][
     i, x]*\((\[HBar]^2\ )\) D[D[\[Psi][i, x], x], 
     x] \[DifferentialD]x\)\)

and then

deltax[i_, x_] := Sqrt[mediex2[i, x] - mediex[i, x]^2]
deltap[i_, x_] := Sqrt[mediep2[5, x] - (mediep[5, x])^2]

and

relatie[5, x] // PowerExpand // FullSimplify
% // N
POSTED BY: Hans Dolhaine
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract