Re: Need help in Calculating Wavefunction Variance


"kp" <4vector@xxxxxxxxx> wrote in message news:d4f44a45-8729-42b6-825d-3ef54c8af6ba@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Apr 30, 12:26 am, kp <4vec...@xxxxxxxxx> wrote:
On Apr 29, 11:49 pm, kp <4vec...@xxxxxxxxx> wrote:

> Well according to mathematica your Eq.2 is wrong. I didn't go
> further.

> kp

I take that back Eq. 2 seems OK.

And your Fourier Transform seems ok. But in your expectation value of
<p^2> you need to take the complex conjugate of the wave-function and
the wave-function itself not just the square of the wave-function.
kp

Thanks! Jay

PS: The mathematica results confirm that the relationship between A and B does not affect the integral. Put another way, if you calculate the integral with A and B as completely free parameters, and then plug in constraining values for A and B, including making them a function of x, and / or of each other, the result is the same whether you plug in the A and B values before or after the integration.

Since this is not always so for integration of inter-dependent variables generally, I suppose this is a consequence of the fact that the definite Gaussian integrals taken from -oo to +oo over dx, are independent of x.

Jay.

.

Relevant Pages

  • Re: LISP routines to do symbolic differentiation
    ... But, I've tried Mathematica to integrate the function I have, ... methods other than indefinite integration, ... For the integration in the present thread, I'm guessing you want to do ... to find antiderivatives using genetic programming, ...
    (comp.lang.lisp)
  • not a bug in integrate, Mma 6.0. But simplfication/assumptions
    ... You will need mathematica 6.0 or 5.* to try this. ... Integration is not, I think, inherent in the problem. ... expressions with assumptions is an issue, or that the Mma operation S/. ... but one generic to other computer algebra systems [most of which I ...
    (sci.math.symbolic)
  • Re: A trap: TWO HOWLERS in Mathematica 6 making a dangerous match
    ... divergent integral not realizing that it diverges... ... (* Mathematica 6 returns an invalid answer, ... any warning message, the first defect. ... first trouble, for both symbolic and numeric integration, is the ...
    (sci.math.symbolic)
  • Re: Optimizing/minimizing functions that use absolute value.
    ... with both differentiation and integration of absreal itself: ... This is a difficult problem for computer algebra systems. ... Mathematica and Derive, and neither is able to do this symbolically. ... I could be wrong; the numerical integration ...
    (sci.math.num-analysis)
  • Re: A continuous antiderivative for the floor function
    ... integration. ... this thread was inspired by a question asked in the Mathematica ... elementary functions first, Mathematica can then give an antiderivative ... in closed form. ...
    (sci.math)