A wavefunction for a particle confined in some region of space is given by the expression:
φ(x)=Asin^2(αx)+Bx^(-2)
What are the dimensions (i.e., units) of A and B?

Question

A wavefunction for a particle confined in some region of space is given by the expression: 
φ(x)=Asin^2(αx)+Bx^(-2)
What are the dimensions (i.e., units) of A and B?

irishboy123 · Answer

@osprey

adamaero · Answer

Sin(x) is odd: f(–x) = –f(x) A squared function is even. Wolfram Alpha says it has even parity...whatever that means. https://www.wolframalpha.com/input/?i=y+%3D+sin%5E2(x)%2BBx%5E-2 The graph looks like this: https://www.wolframalpha.com/input/?i=plot+sin%5E2(x)%2Bx%5E-2

killemall · Answer

Wave functions are used to show probabilities, so they don't have units.

irishboy123 · Answer

$\large \Psi (x)=Asin^2(\alpha x)+\dfrac{B}{x^2}$, right?!


and you're gonna normalise this as 

$\large \int\limits_{-\infty}^{\infty} |\Psi|^2 dx = 1$ ....which is  unitless

using dimensional analysis...

the integration amounts to $\Sigma |\Psi|_i^2 ~ dx_i$, and being unitless means that $\Psi$ has units $\dfrac{1}{\sqrt{m}}$ as $dx_i$ has units $m$

A must have the same units as sine is unitless

$\dfrac{B}{m^2} \equiv \dfrac{1}{\sqrt{m}}$ means B has units $m^{3/2}$

so i reckon ...