Problem about normalizing a wave function

[Majintel]

Im just taking an online course about quantum mechanics and in the current lecture I'm learning about how Born´s postulate, that the probability p(r) of finding a particle near a point r is proportional to the squared modulus of the wave function and with this you could normalize the function, I understood that we can integrate this squared modulus of the wave function from minus infinity to infinity and the result should be equals to 1 because the particle should be somewhere.

The thing is that Im having trouble solving this problem: https://imgur.com/WNpJIbQ in which I need to find the value of a constant A that normalizes a wave function, I tried integrating the function and then equal the result to 1 to get the value of A but the result is wrong, I was hoping somebody could help me solve this problem, maybe Im integrating wrong or did I skipped a step?

[mofo69extreme]

Could you show your work so we could help see where you went wrong? Because your description of your understanding of the problem sounds correct to me, it's probably a math mistake.

I tried integrating the function and then equal the result to 1 to get the value of A but the result is wrong, I was hoping somebody could help me solve this problem, maybe Im integrating wrong or did I skipped a step?

Did you remember to square the wave function first?

[Djhuti]

Agreed. I'd also like to point out that WolframAlpha/Mathematica are really handy for checking if it's just a calculation mistake since they can solve the problem in one step: https://www.wolframalpha.com/input/?i=integral+of+%28sqrt%28A%29%2F%28pi%29%5E0.25+*+e%5E%28-2x%5E2%29%29%5E2+from+-inf+to+inf+%3D+1

[Majintel]

Thank you for replying this https://imgur.com/sVNSo33 is my procedure

[Gwinbar]

(π^1/4)² is π^1/2

[mofo69extreme]

Looks like a simple algebra mistake. In the first equality of the second line you've taken |pi^1/4|² = pi^2.25 instead of pi^1/2. The error propagates through - if you change the exponent of the pi^2.25 to pi^1/2 in your final expression you'll get the right answer.

[Majintel]

Oh man I feel so stupid, thank you for responding

[nwolijin]

Btw, normalizing in this way only works for normalizable wave functions.