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angelamirga332
angelamirga332
01.11.2019 • 
Physics

Aparticle of mass m lives in a one-dimensional infinite square potential well that contains a delta-function division barrier; the corresponding potential can be written as v (x) = { +[infinity], |x| > a, (~ 2/m)γ δ(x), |x| < a, (5) where γ and a are given positive parameters. we are interested in the ground state of the particle in this potential. derive a (transcendental) equation that would allow you to find the energy of the ground state. illustrate how you use the graphical approach to look for solutions of this equation. (c) as the delta-function parameter y varies, that would presumably affect the "communi- cation" between two halves of the potential well in (5). based on general considerations, sketch the evolution of the shapes of the ground state wave function from the "very weak" to the "very strong" division barrier. based on your quantitative analysis in item (b), what is the dimensionless system parameter that actually determines if the division barrier is strong or not. (d) in the limit of a very strong division barrier (is as big as you want but not infinite), find (approximately) the energy of the ground state as a function of y.

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