I got some questions about QM (not well organized) There is wave-particle duality. To my understanding, particle can behave as billard ball and wave. Is the wave property means that we can represent the particle by wavefunction ? The modulus of wavefunction in Schrodinger equation is interpreted by Max Born as probability density. So I guess Schrodinger did not know the meaning of wavefunction when he first proposed it ? How did Max Born comes with the idea that |psi|^2 is the probability density ? (any experiments to verify the probability density ?) In learning quantum mechanics, what I know is to promote classical observable (not sure) to operator, then we formulate the QM problem. But how is it actually done ? e.g. how Schordinger writes down the equation ?