Two-dimensional hydrogen atom in a strong magnetic field

Zeeman Effect in Phase Space

“…before a solution for Eq. (41). Using the orthogonality relations φ * n (q 1 , p 1 )φ m (q 1 , p 1 )dq 1 dp 1 = δ n,m ,…”

Two-dimensional hydrogen-like atom in a uniform magnetic field: Large-order perturbation theory

“…The two-dimensional hydrogen-like atom in a uniform magnetic field perpendicular to the atomic plane has received considerable attention as a model for excitons in thin materials such as nano-scale multilayer semiconductor systems. The Schrödinger equation is separable in polar coordinates and has been solved approximately in many different ways [1][2][3][4][5][6][7][8][9][10][11][12][13]. Here we are interested in the application of perturbation theory that provides approximate solutions in terms of power series of the field strength that are suitable in the weak-field limit [3,8,[10][11][12][13].…”

“…Several authors have obtained perturbation corrections of low order [3,8,10,11,13] but the most extended calculation was due to Szmytkowski [13] who solved the perturbation equations of first and second order by means of Green functions. His analytical results, which are valid for all quantum numbers, suggest that some of the earlier results [10][11][12] may be wrong.…”

Двумерное Кулоновское Рассеяние Квантовой Частицы: Низкоэнергетические Асимптотики

“…Для всего спектра нерелятивистских связанных состояний в работе [3] вычислены дипольные матричные элементы; выведены формулы, определяющие вероятность одно-и двухфотонных переходов между такими состояниями; исследованы сдвиги собственных значений, В. В. ПУПЫШЕВ порожденные включением постоянного электрического поля, и выявлено сверхтонкое расщепление собственных значений. Анализ спектра двумерного атома водорода в сильном магнитном поле выполнен в работе [6].…”