In this article we will rigorously define this problem and find the solutions to the corresponding Schrödinger wave equation, and thenĮxamine some of the properties and implications of these solutions. However constrained to this region, and cannot under any circumstances be found outside of it. What this means in the 1D case, which we examine here, is that there is a particle that is free to move back and forth alongĪ line in between two points (e.g. In its simplest form the problem is one-dimensional (1D), and involves a single particle living in an infinite potential well. As such it is often encountered in introductory quantum mechanics material as a demonstration of the quantization of energy.
The particle in a box or infinite square well problem is one of the simplest non-trivial solutions to Schrödinger's wave equation. Classically the particle is allowed to have any non-negative value for its kinetic energy, including zero.
With constant kinetic energy it bounces back and forth between the walls at x = 0 and x = L. Figure 1: The classical view of a particle (with velocity v) in a 1D box.
