1D Motion of a Quantum Particle

Our goal is to make quantum formalism accessible, proposing it in a simplified form, to show how we arrive at completely different results from those described in the previous section. To describe the dynamics of a quantum particle, we introduce the Schrödinger equation in a discretized space-time, so as to overcome the problems related to differential calculus, presenting it as a wave equation for a two-dimensional vector field (the real part and the imaginary of the wave function). The more familiar concept of vector in the plan is used precisely to avoid the use of complex variables, another subject not yet mastered by high school students. We assume that space is a large one-dimensional lattice with 2N + 1 sites and with a very small pitch and assume that the mass of the particle and the universal constant are equal to 1.

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