Методические материалы

$\\ n = 1, 2, 3, ..., \infty \\ l = 0, 1, ..., (n-1) \\ m_l = -l, ..., 0, ..., +l \\ m_s =\pm \frac{1}{2} \\ E = \frac{mc^2}{\sqrt{1-\beta^2}}, \beta = \frac{v}{c} \\ \vec{p} = \frac{m\vec{v}}{\sqrt{1-\beta^2}} \\ E = \sqrt{p^2c^2+m^2c^4} \\ m_e = 0.511 \ MeV\\ m_p = 938 \ MeV\\ m_n = 939 \ MeV\\ \hat{J}\Psi = J (J+1) \Psi, \ \ J = 0, \frac{1}{2}, 1, \frac{3}{2}, ... \\ \hat{l}\Psi = l (l+1) \Psi, \ \ l = 0, 1, 2, 3, ... \\ E(A, Z) = Zm_p + (A-Z)m_n - M(A, Z) \\ E(A, Z) = a_1A - a_2 A^{\frac{2}{3}} - a_3 \frac{Z(Z-1)}{A^\frac{1}{3}} - a_4 \frac{(A-2Z)^2}{A} + \delta a_5 A^{-\frac{3}{4}} \\ a_1 = 15.78 \ a_2 = 17.8 \ a_3 = 0.71 \ a_4 = 23.7 \ a_5 = 34 \ (MeV) \\ \frac{Z^2}{A} > 17 \\ \vec{j} = \vec{l} + \vec{s} \\ \vec{J} = \sum_{i=1}^A{\vec{j}_i} = \sum_{i=1}^A{(\vec{l}_i+\vec{s}_i)} \\ \frac{e \hbar}{2m_e}, \frac{e \hbar}{2m_p} \\$

$\\ \hat{J}^2\Psi =\hbar J (J+1) \Psi, \ \ \hat{J}_z \Psi = \hbar J_z \Psi \ \ |\vec{J}| = \hbar \sqrt{J(J+1)} \\ \hat{S}^2 \Psi = \hbar^2 S (S+1) \Psi, |\vec{S}| = \hbar \sqrt{s(s+1)} = \frac{\sqrt{3}}{2} \hbar \\ \vec{F} = \vec{A} + \vec{B} \\ |\vec{F}| =\underbrace{A + B, A + B - 1, ..., |A-B|}_{2A+1, \ A \leq B } \\ \varepsilon = \frac{\hbar^2}{2m} (\frac{2m}{a})^2 R_f^2 = \frac{\hbar^2}{2m} (\frac{2m}{a})^2 (n_x^2 + n_y^2 + n_z^2) \\ \frac{m_p}{m_e} = 1836.15 \pm 0.05 \approx 6 \pi^5 \\ \vec{\mu}_d = \vec{l}_p + g_p \vec{s}_p + g_n \vec{s}_n$

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Конспект Саши