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Консультация № 191945

29.11.2017, 19:39

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Образование

Здравствуйте! У меня возникли сложности с таким вопросом:

При каком отношении высоты U0 низкого потенциального барьера бесконечной ширины и энергии E электрона, падающего на барьер, коэффициент отражения ρ=0,5?

Обсуждение

давно

Посетитель
226425
1567

30.11.2017, 23:17

общий

это ответ

Здравствуйте, serzhant.nat!
Дано:
R=0.5
Найти:
U₀/E
Решение:
Формула коэффициента отражения электрона от потенциального барьера получается на основании уравнений Шрёдингера. Её вывод достаточно громоздкий и при необходимости его можно посмотреть например здесь (см. стр.4, формулы 27,28). В рамках данной рассылки приведем ее в готовом виде:
R=[(1-[$627$])/(1+[$627$])]² (1) - коэффициент отражения,
здесь параметр [$627$] определяется как
[$627$]=[$8730$][(E-U₀)/E] (2)
Итак, сначала работаем с формулой (1)
Извлекаем корень из лев. и пр. частей
[$8730$]R=(1-[$627$])/(1+[$627$])
Домножаем на знаменатель, приводим подобные, выносим за скобки параметр [$627$]
[$627$](1+[$8730$]R)=1-[$8730$]R
Можно подставить значение R и подсчитать значение [$627$]
[$627$]=(1-[$8730$]0,5)/(1+[$8730$]0,5 = 0,1716
Согласно формуле (2)
0,1716 = [$8730$](E-U₀)/E
Возведем в квадрат
(E-U₀)/E = 0.02944
E-U₀ = 0,02944*E
E(1-0,02944) = U₀
И, наконец,

U₀/E = 0,971

p/s. Для решения этой задачи оказалось мало одной конфеты... пришлось заточить еще и пачку вафель

5

Об авторе:
С уважением
shvetski

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