Momentum representation in quantum mechanics ($\varphi (k)=(2\pi {)}^{-1/2}\int \psi (x)e^{-ikx}dx$)

The Fourier transform in the title represents a one-dimensional state in the wavevector basis. Its probability density is $|\varphi (k){|}^2$, normalized by $\int |\varphi (k){|}^{2}dk=1$ when $\int |\psi (x){|}^{2}dx=1$. For physical momentum $p=\hslash k$, the density per unit momentum is $|\varphi (p/\hslash ){|}^2/\hslash$. A confined stationary energy eigenstate need not be a momentum eigenstate.