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A potential barrier of the kind studied by Fowler and others may be represented by the analytic function V (Eq. (1) ). The Schr\"odinger equation associated to this potential is soluble in terms of hypergeometric functions, and the coefficient of reflection for electrons approaching the barrier with energy W is calculable (Eq. (15) ). The approximate formula, 1-=exp-4{h (2m (V-W) ) ^1{2}dx} is shown to agree very well with the exact formula when the width of the barrier is great compared to the de Broglie wave-length of the incident electron, and W<V₌₀ₗ.
Carl Eckart (Sun,) studied this question.
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