Computing Inner Product of f_1 Using Maple Procedure

[latentcorpse]

so I'm writing a maple procedure for the variational principle in quantum mechanics.

i have a function $f_1(x,\alpha)=\cos{\alpha x}$ for $|x| \leq \frac{\pi}{2 \alpha}$ and i need to compute $\left \langle f_1 | f_1 \right \rangle$

i have the code:

restart;
assume(x,real);
assume(hbar,positive);
assume(omega,positive);
assume(e,positive);
assume(alpha,positive);
assume(m,positive);
f1:=cos(alpha*x);
conjf1:=conjugate(f1);
normaliseint:=int(conjf1*f1,-Pi/(2*alpha)..Pi/(2*alpha));

now the andwer should be $\frac{\pi}{2}$ (i did it by hand) but Maple keeps giving me

$1/2\, \left( 2\,\cos \left( 1/2\,{\frac {\pi }{{\it \alpha}}} \right) \sin \left( 1/2\,{\frac {\pi }{{\it \alpha}}} \right) {\it \alpha}+\pi \right) {{\it \alpha}}^{-1}$

any ideas?
thanks.

 

[NateD]

The answer you are getting is correct. When you integrate a function over a finite domain, the integral will not necessarily be equal to the exact answer. The answer you got is the approximate integral of the function over the given domain.

 

[oswaler]

I would first commend you for using a computational tool like Maple to assist in your research on the variational principle in quantum mechanics. It is important to embrace technology in scientific research to increase efficiency and accuracy.

In regards to your question, the inner product of f_1 can be computed using the Maple procedure as follows:

1. First, we need to define the function f_1(x, alpha) in Maple using the "f1" variable. This can be done using the ":= " operator as shown in your code.

2. Next, we need to define the conjugate of f_1, which can be done using the "conjugate" function in Maple. This will be stored in the "conjf1" variable.

3. Then, we can compute the inner product using the "int" function in Maple, which represents the integration symbol. The limits of integration should be set to -Pi/(2*alpha) and Pi/(2*alpha) as shown in your code.

4. Finally, we can simplify the expression using the "simplify" function in Maple. This will give us the desired result of pi/2.

It is important to note that the result may appear different from what you calculated by hand due to the nature of symbolic computation. However, the result is mathematically equivalent and accurate.

I hope this helps in your research and further exploration of quantum mechanics. Keep up the good work!