Wave functions are more than "probability waves", though ( more properly, probability **amplitudes**, as it is the square modulus that corresponds to probability density - just as it is the square modulus of radiation amplitude that gives the radiation intensity).

The wave function also contains within it the other properties of the entity, which can be extracted by use of the appropriate operator.

'sigh'. I kinda hate to say this, but that's all a bit misleading.

To operate on a state, you need something physical--an electric or magnetic field, a photon tuned to a particular frequency. You need to have the particle you want to manipulate,

*interact* with a physical field. This is how qubit operations on IBMs quantum computer are realised--the photons are in the microwave region.

There is no intrinsic mass, charge, or spin in the equation $$ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $$. To see operators, you will need to know something about particle energies; you need Hamiltonians.

I have no idea how to recover mass, charge, or spin from a pair of complex

*numbers*.

It's important to realise that the wavefunction is not physical, it says nothing at all about physical fields. Also, the above equation describes a real complex amplitude for "a particle", it doesn't need to say

**what kind** of particle. Maybe that will help.

So, for the younger viewers, the probability amplitudes of particles can be manipulated, but, you have to manipulate a real, physical particle to achieve this.

Check out (google is your friend) how IBM manipulates complex probability amplitudes of real particles trapped in a cavity. The physics is what determines how the amplitudes change; it's as if the complex amplitudes follow the particles around!