A particle with an energy of 20.0 eV is initially travelling in a region in which the potential energy is zero. The particle is incident upon a potential energy barrier which has a height of 14.0 eV. Treat this problem quantum mechanically. What is the probability that the particle will be reflected by the barrier? What is the probability that the particle will be transmitted past the barrier?

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Connection formulae for WKB approximation

In quantum mechanics, Schrödinger’s equation for certain systems with varying parameters cannot be solved directly. In such a case, an approximation method is used to obtain the approximate solution. WKB method is a special technique used to obtain the approximate solution for Schrödinger’s time-independent equation. In general, the WKB method is used to solve linear differential equations with varying coefficients. This method is called semiclassical approximation in quantum mechanics.