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Консультация № 183100
09.05.2011, 00:39
50.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Электрон в одномерной прямоугольной «потенциальной яме» шириной l=100пм с бесконечно высокими «стенками» находится в возбужденном состоянии (п=4). Определите: а) минимальную энергию электрона; б) вероятность W обнаружения электрона в средней трети «ямы».
Электрон в одномерной прямоугольной «потенциальной яме» шириной l=100пм с бесконечно высокими «стенками» находится в возбужденном состоянии (п=4). Определите: а) минимальную энергию электрона; б) вероятность W обнаружения электрона в средней трети «ямы».
Обсуждение
09.05.2011, 05:56
общий
это ответ
Здравствуйте, alya_koshka!
а) Энергия частицы массы m, находящейся в одномерной прямоугольной потенциальной яме шириной l с бесконечно высокими стенками в квантовом состоянии n, определяется выражением
В данном случае n=4, m = m[sub]e[/sub] = 9.11·10[sup]-31[/sup] кг, l = 100 пм = 10[sup]-10[/sup] м и минимальная энергия электрона равна E = (6.626·10[sup]-31[/sup])[sup]2[/sup]*4[sup]2[/sup]/(8*9.11·10[sup]-31[/sup]*(10[sup]-10[/sup])[sup]2[/sup]) [$8776$] 9.64·10[sup]-17[/sup] Дж.
б) Движение частицы, находящейся в одномерной прямоугольной потенциальной яме шириной l с бесконечно высокими стенками в квантовом состоянии n, описывается волновой функцией
Распределение плотности вероятности по координате x определяется квадратом модуля волновой функции |[$936$](x)|[sup]2[/sup]. Поэтому
В данном случае n=4, a = l/3, b = 2l/3, (b-a)/l = 1/3, (a+b)/l = 1 и искомая вероятность равна
а) Энергия частицы массы m, находящейся в одномерной прямоугольной потенциальной яме шириной l с бесконечно высокими стенками в квантовом состоянии n, определяется выражением
В данном случае n=4, m = m[sub]e[/sub] = 9.11·10[sup]-31[/sup] кг, l = 100 пм = 10[sup]-10[/sup] м и минимальная энергия электрона равна E = (6.626·10[sup]-31[/sup])[sup]2[/sup]*4[sup]2[/sup]/(8*9.11·10[sup]-31[/sup]*(10[sup]-10[/sup])[sup]2[/sup]) [$8776$] 9.64·10[sup]-17[/sup] Дж.
б) Движение частицы, находящейся в одномерной прямоугольной потенциальной яме шириной l с бесконечно высокими стенками в квантовом состоянии n, описывается волновой функцией
Распределение плотности вероятности по координате x определяется квадратом модуля волновой функции |[$936$](x)|[sup]2[/sup]. Поэтому
В данном случае n=4, a = l/3, b = 2l/3, (b-a)/l = 1/3, (a+b)/l = 1 и искомая вероятность равна
5
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