Can you normalize a free particle?

The probability of finding the particle somewhere in all space is 1, but infinitesimal in any finite interval. As you found, to normalize this solution, the amplitude must be infinitesimal. If you combine two components, the probability distribution is not uniform.

What is the wave function for a free particle?

The wave function ψ(x, t) of a free particle is. ψ(x, t) = 1. √ 2πh.

What does it mean to normalize a wave function?

Essentially, normalizing the wave function means you find the exact form of that ensure the probability that the particle is found somewhere in space is equal to 1 (that is, it will be found somewhere); this generally means solving for some constant, subject to the above constraint that the probability is equal to 1.

Why wave function should be Normalised?

Since wavefunctions can in general be complex functions, the physical significance cannot be found from the function itself because the √−1 is not a property of the physical world.

Why is it not possible to normalize the free particle/wave functions over the whole range of motion of the particle?

The integral does not converge, thus when the normalization integral of the wave functions is evaluated, it does not converge. Therefore the wave functions cannot be normalized over the entire range of motion of the particle.

Why free particles are not Normalizable?

By “not normalizable” we mean that there is no value of A that makes the following integral true: which makes the total probability of finding the particle somewhere equal to 1. It simply means that the wave function given above is not actually a valid wave function for a free particle, strictly speaking.

What is the equation of motion of a free particle?

This wave has a frequency and wave vector k = p / ℏ (the corresponding wavelength λ = 2 π ℏ / p is called the de Broglie wavelength of the particle). The energy spectrum of a freely moving particle is thus found to be continuous, extending from zero to +∞.

Why must the wave function of a particle be normalized?

The reason why we normalize a wavefunction is the same reason why we should normalize a probability distribution. In position space for example, the inner product of a wave function and itself gives the probability of observing the object at the point in space.