Claude Cohen-Tannoudji - Quantum Mechanics, Volume 3

Здесь есть возможность читать онлайн «Claude Cohen-Tannoudji - Quantum Mechanics, Volume 3» — ознакомительный отрывок электронной книги совершенно бесплатно, а после прочтения отрывка купить полную версию. В некоторых случаях можно слушать аудио, скачать через торрент в формате fb2 и присутствует краткое содержание. Жанр: unrecognised, на английском языке. Описание произведения, (предисловие) а так же отзывы посетителей доступны на портале библиотеки ЛибКат.

Quantum Mechanics, Volume 3: краткое содержание, описание и аннотация

Предлагаем к чтению аннотацию, описание, краткое содержание или предисловие (зависит от того, что написал сам автор книги «Quantum Mechanics, Volume 3»). Если вы не нашли необходимую информацию о книге — напишите в комментариях, мы постараемся отыскать её.

This new, third volume of Cohen-Tannoudji's groundbreaking textbook covers advanced topics of quantum mechanics such as uncorrelated and correlated identical particles, the quantum theory of the electromagnetic field, absorption, emission and scattering of photons by atoms, and quantum entanglement. Written in a didactically unrivalled manner, the textbook explains the fundamental concepts in seven chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications.<br> <br> * Completing the success story: the third and final volume of the quantum mechanics textbook written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloë<br> * As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly<br> * Comprehensive: in addition to the fundamentals themselves, the books comes with a wealth of elaborately explained examples and applications<br> <br> Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the Collège des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms.<br> <br> Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics.<br> <br> Franck Laloë was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.<br>

Quantum Mechanics, Volume 3 — читать онлайн ознакомительный отрывок

Ниже представлен текст книги, разбитый по страницам. Система сохранения места последней прочитанной страницы, позволяет с удобством читать онлайн бесплатно книгу «Quantum Mechanics, Volume 3», без необходимости каждый раз заново искать на чём Вы остановились. Поставьте закладку, и сможете в любой момент перейти на страницу, на которой закончили чтение.

Тёмная тема
Сбросить

Интервал:

Закладка:

Сделать

(66) The variations 65are therefore acceptable for any real value of χ We now - фото 1034

The variations (65)are therefore acceptable, for any real value of χ .

We now compute how they change the operator картинка 1035defined in (40). In the sum over k , only the k = l and k = m terms will change. The k = l term yields a variation:

(67) whereas the k m term yields a similar variation but where is replaced by - фото 1036

whereas the k = m term yields a similar variation but where Quantum Mechanics Volume 3 - изображение 1037is replaced by Quantum Mechanics Volume 3 - изображение 1038. This leads to:

(68) We now include these variations in the three terms of 61 as the - фото 1039

We now include these variations in the three terms of (61); as the distributions f are unchanged, only the terms картинка 1040and will vary The infinitesimal variation of is written as 69 A - фото 1041will vary. The infinitesimal variation of is written as 69 As for it contains two contributions one - фото 1042is written as:

(69) As for it contains two contributions one from and one from - фото 1043

As for картинка 1044, it contains two contributions, one from картинка 1045and one from картинка 1046. These two contributions are equal since the operator W 2(1,2) is symmetric (particles 1 and 2 play an equivalent role). The factor 1/2 in disappears and we get 70 We can regroup these two contributions using the - фото 1047disappears and we get:

(70) We can regroup these two contributions using the fact that for any operator O - фото 1048

We can regroup these two contributions, using the fact that for any operator O (12), it can be shown that:

(71) This equality is simply demonstrated 5 by using the definition of the partial - фото 1049

This equality is simply demonstrated 5 by using the definition of the partial trace Tr 2{ O (1,2)} of operator O (1, 2) with respect to particle 2. We then get:

(72) Inserting now the expression 68for we get two terms one proportional to - фото 1050

Inserting now the expression (68)for we get two terms one proportional to eiχ another one to eiχ whose value - фото 1051, we get two terms, one proportional to eiχ , another one to e–iχ , whose value is:

(73) Now for any operator O 1 we can write 74 so that the variation 73can - фото 1052

Now, for any operator O (1), we can write:

(74) so that the variation 73can be expressed as 75 The term in eiχ has a - фото 1053

so that the variation (73)can be expressed as:

(75) The term in eiχ has a similar form but it does not have to be computed for the - фото 1054

The term in eiχ has a similar form, but it does not have to be computed for the following reason. The variation Quantum Mechanics Volume 3 - изображение 1055is the sum of a term in eiχ and another in e–iχ :

(76) Quantum Mechanics Volume 3 - изображение 1056

and the stationarity condition requires картинка 1057to be zero for any choice of Choosing χ = 0, yields c 1+ c 2= 0; choosing χ = π/2, and multiplying by – i , we get c 1– c 2= 0. Adding and subtracting those two relations shows that both coefficients c 1and c 2must be zero. Consequently, it suffices to impose the terms in e±iχ , and hence expression (75), to be zero. When the distribution functions fβ are not equal and we get 77 if - фото 1058, the distribution functions are not equal, and we get:

(77) if however we have not yet obtained any particular condition to be - фото 1059

(if картинка 1060, however, we have not yet obtained any particular condition to be satisfied 6 ).

β. Variation of the energies

Let us now see what happens if the energy картинка 1061varies by картинка 1062. The function картинка 1063then varies by Quantum Mechanics Volume 3 - изображение 1064which, according to relation (40), induces a variation of Quantum Mechanics Volume 3 - изображение 1065:

Читать дальше
Тёмная тема
Сбросить

Интервал:

Закладка:

Сделать

Похожие книги на «Quantum Mechanics, Volume 3»

Представляем Вашему вниманию похожие книги на «Quantum Mechanics, Volume 3» списком для выбора. Мы отобрали схожую по названию и смыслу литературу в надежде предоставить читателям больше вариантов отыскать новые, интересные, ещё непрочитанные произведения.


Отзывы о книге «Quantum Mechanics, Volume 3»

Обсуждение, отзывы о книге «Quantum Mechanics, Volume 3» и просто собственные мнения читателей. Оставьте ваши комментарии, напишите, что Вы думаете о произведении, его смысле или главных героях. Укажите что конкретно понравилось, а что нет, и почему Вы так считаете.

x