You can use np.apply_along_axis:
np.apply_along_axis(function, 1, array)
The first argument is the function, the second argument is the axis along which the function is to be applied. In your case, it is the first axis. The last argument is the array, of course.
You should be warned, however, that apply_along_axis is only a convenience function, not a magic bullet. It has a severe speed limitation, since it just hides a loop. You should always try to vectorize your computation, where possible. Here’s how I’d do this:
v = array[:, 0] ** 2 # computing just once
return np.exp((-v / 200) - 0.5 * (array[:, 1] + 0.05 * v - 5) ** 2)