Fourier Transform Momentum Space

Show activity on this post.

Fourier transform momentum space.

ϕ k 1 2 π 3 r space ψ r e i k r d 3 r. Fourier transform of gaussian. What this answer explains is that to find the general time dependent solution you can t simply find the states of definite momentum and tack on the time dependence as you would for the free particle since the states of definite momentum are not in. Analogous to a signal this ψ can be written as either a momentum space wave function or a position space wave function.

For momentum space and. We wish to fourier transform the gaussian wave packetin momentum k spaceto get in position space. Now we will transform the integral a few times to get to the standard definite integral of a gaussian for which we know the answer. The fourier transform formula is.

ψ r 1 2 π 3 k space ϕ k e i k r d 3 k. The interpretation of the spatial fourier transform yielding momentum originates in quantum mechanics for which we have the relationship p k hbar where hbar is the dirac constant or reduced planck s constant. First which does nothing really since.