Won't Integrate

[Chris Maness]

I think this is the first integral that I have thrown at Sage that
stumps it. Any suggestions on getting this guy to go through.

a=var('a');
assume(a > 0);
k=var('k');
assume(k > 0);
hbar=var('hbar');
assume(hbar > 0);
m=var('m');
assume(m > 0);
t=var('t');
assume(t > 0);
integrate(exp(-k^2/(4*a))*exp(i*k*x-i*hbar*k^2*t/(2*m)),k,-oo,oo)

Chris

[Robert Dodier]

On 2014-07-04, Chris Maness <ch...@chrismaness.com> wrote:

> integrate(exp(-k^2/(4*a))*exp(i*k*x-i*hbar*k^2*t/(2*m)),k,-oo,oo)

Well, I see the integrand is a quadratic (with constant term = 0) in k,
so you can try integrate(exp(A*k^2 + B*k), k, -oo, oo) (Maxima, and
therefore Sage, can solve that) and then substitute A and B into the
result. You can get A and B via ratcoef(foo, k^2) and ratcoef(foo, k)
where foo is the quadratic (I assume there's a way to call ratcoef).

It's certainly reasonable to expect that Maxima should carry out that
analysis on its own; it's not a bug although it is certainly a drawback.
I don't know if e.g. SymPy could solve it; I didn't try.

best

Robert Dodier