Why Is Calculating the Normalization Constant in Quantum Mechanics Challenging?

[lol physics]

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 = \frac{1}{2^1^/^2} (\frac{a}{\pi})^1/4

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

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

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

any flawless mathematicians out there..?

 

[Redbelly98]

Welcome to Physics Forums

any flawless mathematicians out there..?

Nope ... there's no such thing!

Can you show the integral you set up to calculate A?

 

[lol physics]

any one?

 

[hage567]

If you show more steps of your work, we might be able to spot where you went wrong.

 

[lol physics]

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.

 

[lotrsimp12345]

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.

 

[Redbelly98]

lol physics, I agree that A is proportional to a^-1/4

 

[Matterwave]

If you think the problem is wrong, why don't you just plug in their normalization constant and see if you get 1? If you don't get 1, then there is probably something wrong.

 

[lol physics]

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.