Examining the existence of bound states in a square well using a simple method

The time-independent Schrödinger equation is analytically solved for the square, one-dimensional and symmetrical potential well, in order to demonstrate, using a simple method, that there is at least one bound state in the limiting cases of depth and width of the analyzed system. For a complete analysis, five conditions for the depth and width of the well are required.

Keywords:
Schrödinger equation; Potential well; Bound states