Though quantum mechanics is a dynamical theory much like Newtonian mechanics, there are key differences between the two. In Newton’s mechanics, the state of a particle at t = 0 is specified by giving its initial position x (0) and velocity v (0) – only two numbers; Quantum mechanics demands an entire wavefunction ψ (x, 0) – an infinite set of numbers corresponding to the wavefunction value at every point x. However both theories describe how this state changes with time when the forces acting on the particle are known. In Newton’s mechanics, x (t) and v (t) are calculated from Newton’s second law; in quantum mechanics ψ (x, t) must be calculated from another law – Schrodinger’s equation.
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