Finite Square-well Potential Research Articles

Noninteracting Fermi Gas in a Square-Well Potential

The problem of a noninteracting Fermi gas in a finite square-well potential is solved analytically in the limit that the well becomes infinitely wide. The errors of previous authors using this model as a first approximation to the problem of a simple metal with surfaces are pointed out.

On Boundary Conditions for an Infinite Square-Well Potential in Quantum Mechanics

A well-known problem of an infinite square-well potential in quantum mechanics furnishes an interesting boundary condition. We investigate this in detail by considering the infinite square-well potential as a limiting case of an finite square-well potential.

Bound-State Energies of a Particle in a Finite Square Well: An Improved Graphical Solution

The energy eigenvalues for a particle bound in a finite or semi-infinite square-well potential are shown to be determined by the points of intersection of two straight lines with sine or cosine curves. This construction, which is simple enough for students to remember, can also be used to determine the number of bound states for a given potential strength, and to obtain approximate values for the energies of low-lying states in a deep square well.