# Dimensions of a Projection

1. Sep 22, 2009

### iamalexalright

1. The problem statement, all variables and given/known data
If an arbitrary intial state function for a particle in a box is expanded in the discrete series of eigenstates of the Hamiltonian relevant to the box configuration, one obtains:

$$\psi(x,0) = \Sigma^{\infty}_{n=1}b_{n}(0)\varphi_{n}(x)$$

If the particle is free, we obtain:

$$\psi(x,0) = \int^{\infty}_{-\infty}b(k)\varphi(k)dk$$

(a)
What are the dimensions of:
abs(b_{n})^2
and abs(b(k))^2?

I don't understand what they mean by dimensions! any hints?

2. Sep 23, 2009

### kuruman

By dimensions they mean, well, dimensions as in dimensional analysis in terms of the standard three, Mass, Length and Time. Start by considering

$$\int \psi^{*}(x)\psi(x)\: dx = 1$$

What are the dimensions of ψ(x)? Sort it out from there.