Here, is a complex-valued probability amplitude; and are strictly real.

It is more directly intuitive to have probability amplitudes as functions of space and time.

At every position and time coordinate, the probability amplitude has a value by direct calculation.

Perhaps oddly, this approach is not the most general way to represent probability amplitudes.

The wavefunction represents the probability amplitude of finding the system in that state.

The probability amplitude is given by adding together the contributions of all paths in configuration space.

And this is the confusing quantum bit: we have to add the two probability amplitudes, which can, in fact, be negative.

In physical terms, a spinor should determine a probability amplitude for the quantum state.

This seems to throw away the information in the probability amplitudes.

It is very important for quantum mechanics: see probability amplitude and Born rule.