Quantum Chemistry 3.7 – Particle in a Box Wavefunction Plots

Short lecture demonstrating particle in a box wavefunctions.

The particle in a box is a quantum mechanical model system for a particle which is restricted to a finite region of space. The potential energy is zero inside the box (zero to L) and infinite outside. The energy levels depend quadratically on a quantum number n [ E_n = h^2 n^2 / (8 m L^2) ] which is between 1 and infinity (n = 1, 2, 3, …). The wavefunction is a half-integer number of sine waves inside the box [ psi_n(x) = sqrt(2 / L) sin(n pi x / L) ]. Quantum behavior disappears when you go to sufficiently large values of box length L and/or particle mass m.

Graph: https://www.desmos.com/calculator/zqo7bncevb

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