Physics · Quantum Mechanics

A particle with energy E > 0 is incident from the right (x > 0) on a one-dimensional potential composed of a delta-function barrier at x = 0 and a hard wall at x = -a: V(x) = αδ(x) for x > -a, and ∞ for x ≤ -a, where α > 0 and a > 0. Let us define k2 = 2mE/ℏ2 and the dimensionless quantities: ξ = ka and β = ℏ2/(2mαa). For some energy E, the particle reflects from the barrier without any phase shift. Which of the following transcendental equations determines this energy?