Continuous wave functions seems to be far harder than discrete particles.
True, but consider that discrete particles are a special case of continuous wave functions: The case where the phase-space distribution is a delta function or some very good approximation to it. If you limit your quantum mechanics to cases that classical mechanics can describe well, then you are operating, in effect, on delta functions, and this simplifies the math immensely.
The apparent simplicity of classical mechanics comes from looking only at these special cases; quantum mechanics deals with more general situations, so it is unavoidably more complex. But if you made a quantum-mechanics program to predict only classical situations, it would not necessarily be more complex than the corresponding program using the laws of Newton, who is not forgotten.
True, but consider that discrete particles are a special case of continuous wave functions: The case where the phase-space distribution is a delta function or some very good approximation to it. If you limit your quantum mechanics to cases that classical mechanics can describe well, then you are operating, in effect, on delta functions, and this simplifies the math immensely.
The apparent simplicity of classical mechanics comes from looking only at these special cases; quantum mechanics deals with more general situations, so it is unavoidably more complex. But if you made a quantum-mechanics program to predict only classical situations, it would not necessarily be more complex than the corresponding program using the laws of Newton, who is not forgotten.