Quantum Chemistry 3.5 - Particle in a Box

Short lecture on particle in a box wavefunctions and energies.

The particle in a box is a model system for a particle which is constrained to a finite region of space. The potential energy is zero inside the box (zero to L) and infinite outside the box. We substitute this potential energy function into the Schrodinger equation and solve for the wavefunction and the energy levels of the particle in a box. Using the boundary conditions that the wavefunction must be zero at the edges of the box, we determine that the wavefunctions are a half integer of a sine wave inside the box. The energy depends quadratically on the positive quantum number n (n = 1, 2, 3), inverse with mass, and inverse quadratic with the length of the box.

Notes Slide: http://i.imgur.com/ARoaMTQ.png

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