Delta Potential - Single Delta Potential

Single Delta Potential

The time-independent Schrödinger equation for the wave function ψ(x) of a particle in one dimension in a potential V(x) is

where ħ is the reduced Planck constant and E is the energy of the particle.

The delta potential is the potential

where δ(x) is the Dirac delta function. It is called a delta potential well if λ is negative and a delta potential barrier if λ is positive. The delta has been defined to occur at the origin for simplicity; a shift in the delta function's argument does not change any of the proceeding results.