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Консультация № 202288
11.03.2022, 15:05
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Здравствуйте! Прошу помощи в следующем вопросе:
Волновая функция микрочастицы в одномерной прямоугольной потенциальной яме шириной a=4*10-9 м с бесконечными стенками имеет вид [$936$]=Ах3 (A-x).
Найти координату x микрочастицы в (нм), при которой плотность вероятности её нахождения максимальна.
Варианты ответа: а)1,0 нм б) 1,5 нм в) 2,0 нм г) 2,5 нм д)3,0 нм
Волновая функция микрочастицы в одномерной прямоугольной потенциальной яме шириной a=4*10-9 м с бесконечными стенками имеет вид [$936$]=Ах3 (A-x).
Найти координату x микрочастицы в (нм), при которой плотность вероятности её нахождения максимальна.
Варианты ответа: а)1,0 нм б) 1,5 нм в) 2,0 нм г) 2,5 нм д)3,0 нм
Обсуждение
16.03.2022, 13:44
общий
16.03.2022, 13:45
это ответ
Плотность вероятности p(x) обнаружения частицы в конкретной точке x определяется величиной |[$968$](x)|[sup]2[/sup], которая в данном случае равна
Точку максимума определим из условия p'(x) = 0, то есть
откуда x = 0, x = 3A/4, x = A. Очевидно, что на границах ямы (x = 0 и x = A) плотность будет минимальна (равна нулю), максимум же будет достигаться при x = 3A/4, то есть в данном случае при x = 3 нм. Поэтому правильный ответ - д).
Точку максимума определим из условия p'(x) = 0, то есть
откуда x = 0, x = 3A/4, x = A. Очевидно, что на границах ямы (x = 0 и x = A) плотность будет минимальна (равна нулю), максимум же будет достигаться при x = 3A/4, то есть в данном случае при x = 3 нм. Поэтому правильный ответ - д).
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