Why Is Calculating the Normalization Constant in Quantum Mechanics Challenging?

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Hi, 2nd year physics student here

doing a past paper on quantum mechanics everything is going nice and dandy then this happens..

question: prove that the normalisation constant A is given by A = [tex]\frac{1}{2^1^/^2}[/tex] ([tex]\frac{a}{\pi}[/tex])^1/4

ok seems fairly straight forward but i keep getting this A = [tex]\frac{1}{2^1^/^2 (a*\pi)^1^/^4}[/tex]

wave function ------> [tex]\Psi[/tex] (x,t) = A*2*[a*x*(e^-ax^2/2)(e^-3/2iwt)

useful integral: Inegration from - infinity to + infinity of x[tex]^{2}[/tex]*e[tex]^{-C}[/tex][tex]^{x^{}2}[/tex] dx = [tex]\frac{1}{2}[/tex] ([tex]\frac{\pi}{C^{3}}[/tex])[tex]^{\frac{1}{2}}[/tex]

any flawless mathematicians out there..?
 
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you have the wave function, you have what the answer should be and you have the identity integral needed to solve this. I gave you the answer i kept receiving, my friend who is a theoretical physicist also received the same answer, if you do in fact obtain the right answer can you show a step by step of how it was obtained, if you received the same answer as us then there may be a problem with the actual question.
 
could have something to do with odd functions and even functions. I got a problem like this. It ended up being 0 because it was an odd function and with even functions you double.
 
found the problem sorry, i was reading the question wrongly. you can use this thread as an example of why you should read questions properly, i thought the square root was covering the whole wave function but it was only covering one of the constants. thank you for all your help.