Re: Problems with functions of a Complex Variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg102821] Re: Problems with functions of a Complex Variable*From*: pfalloon <pfalloon at gmail.com>*Date*: Fri, 28 Aug 2009 00:45:54 -0400 (EDT)*References*: <h75nn9$pgc$1@smc.vnet.net>

On Aug 27, 8:38 pm, Sergio Miguel Terrazas Porras <sterr... at uacj.mx> wrote: > Dear Group: > > I am trying to illustrate with Mathematica 7.0.1 some of the concepts of Quantum Mechanics. > > In particular, for the particle in an Infinite Square Well, I define the time dependent Wave Function (Sum of Sines times Complex Exponentials ) Ok. > > Using only the first 3 terms of the series, I run into the following: > > If I use ComplexExpand[ ] I get things of the form a + I b, which, I would assume means to Mathematica that a and b are Real. > > I then ask for the Conjugate of the preceding expresi=F3n, and I get things like Conjugate[a] - I*Conjugate[b]. (??) > > If I plot the Probability Density Function, things are Ok. (Its Real) > > If I try to calculate the (time dependent) expected value of x, Assuming[Element[{x,t},Reals],Integrate[x*psi*Congugate[psi],{x,0,a}] > > Matem=E1tica hangs forever even though its only nine integrals. > > Any help will be very much appreciated. > > Sergio Terrazas Apologies, in the example from my first response I just discovered a slightly smarter way to do the simplification which doesn't require a [n] to be real: In[79]:= (* get the probability density using FunctionExpand -- allows a[n] to be COMPLEX *) absSq[x_,t_] = f[x,t]*Conjugate@f[x,t] // FunctionExpand[#, Element [{x,t},Reals]] & In[80]:= (* now the integral returns sum of a[n]*Conjugate[a[n]] *) Integrate[absSq[x,t],{x,0,1}] Out[80]= a[1] Conjugate[a[1]] + a[2] Conjugate[a[2]] + a[3] Conjugate[a[3]] The function FunctionExpand is very useful in this kind of situation...