Atomic field shifts and spectral differences
GRE Subject Test · GRE Physics Topic 40 7:50 English narration · English + 中文 subtitles burned in
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The same magnetic field needs different quantum labels once its energy becomes larger than the spin-orbit splitting.
当磁场能量超过自旋-轨道分裂时，同一个磁场就需要用不同的量子数来描述。
This topic computes magnetic shifts in each coupling regime, finds the shifts of spectral lines from upper and lower levels, and contrasts parity cancellation with electric-field splitting of degenerate states.
本主题在不同耦合区计算磁致能移，由上下能级求出谱线的移动，并比较宇称导致的抵消与简并态在电场中的分裂。
An electron has a negative magnetic moment: mu sub L equals negative mu sub B times L over h-bar, and mu sub S is approximately equal to negative 2 mu sub B times S over h-bar.
电子具有负磁矩：μ_L = −μ_B L / ℏ，且 μ_S ≈ −2μ_B S / ℏ。
With B along positive z, the interaction minus mu dot B therefore gives H sub Z equals mu sub B times B times open parenthesis L sub z plus 2 S sub z close parenthesis over h-bar.
当磁场 B 沿正 z 方向时，相互作用 −μ·B 给出 H_Z = μ_B B(L_z + 2S_z) / ℏ。
Mu sub B is approximately equal to 5.788 times 10 to the minus 5 eV per T.
μ_B 约等于 5.788×10⁻⁵ eV/T。
In an uncoupled basis with orbital projection m sub l and spin projection m sub s equals plus or minus one half, the shift is mu sub B times B times open parenthesis m sub l plus 2 m sub s close parenthesis.
在轨道投影为 m_l、自旋投影为 m_s = ±1/2 的无耦合基底下，能移为 μ_B B(m_l + 2m_s)。
Use this uncoupled rule when the magnetic interaction is large relative to the relevant spin-orbit splitting but still small relative to orbital energy gaps, so quadratic diamagnetic and orbital restructuring effects can be neglected.
当磁相互作用相对于相关的自旋-轨道分裂较大，但相对于轨道能隙仍较小时，可使用此无耦合规则，从而忽略二次抗磁效应和轨道重组效应。
Large and small are comparisons of energies, not universal Tesla thresholds.
大与小是能量的比较，而非通用的特斯拉阈值。
In the opposite weak-field regime, m sub l and m sub s are not independently conserved labels for an LS-coupled eigenstate.
在相反的弱场极限下，m_l 和 m_s 不再是 LS 耦合本征态中独立守恒的量子数标签。
When LS coupling dominates a weak magnetic perturbation, J equals L plus S and m sub J labels the multiplet.
当LS耦合主导弱磁场微扰时，J等于L加S，m_J标记多重态。
The first-order shift is mu sub B times B times g sub J times m sub J, with g sub J equals 1 plus J times J plus 1 plus S times S plus 1 minus L times L plus 1 all over 2 times J times J plus 1 in the approximation g sub s equals 2.
一级位移为μ_B乘以B乘以g_J乘以m_J，其中g_J等于1加上J乘J加1加S乘S加1减L乘L加1除以2乘J乘J加1，近似条件为g_s等于2。
L, S, and J here are dimensionless quantum numbers.
此处L、S和J均为无量纲量子数。
For L equals 1 and S equals one half, J equals three halves gives g sub J equals four thirds and shifts minus 2, minus two thirds, plus two thirds, plus 2 times mu sub B times B.
对于L等于1、S等于二分之一，J等于二分之三给出g_J等于三分之四，位移分别为负2、负三分之二、正三分之二、正2倍μ_B乘以B。
J equals one half gives g sub J equals two thirds and shifts plus or minus mu sub B times B divided by 3.
J等于二分之一给出g_J等于三分之二，位移为正负μ_B乘以B除以3。
Do not substitute J equals 0 into the singular formula; a J equals 0 state has no first-order vector projection shift.
不要将J等于0代入该奇异公式；J等于0的态没有一级矢量投影位移。
Intermediate fields require a coupled Hamiltonian rather than mixing weak-field and uncoupled formulas.
中间场需要采用耦合哈密顿量，而非混合弱场与未耦合公式。
A photon's energy is the upper atomic energy minus the lower energy.
光子的能量等于上能级能量减去下能级能量。
Its field-induced change is therefore delta E sub gamma equals delta E sub upper minus delta E sub lower.
因此，其感生场变化为 ΔE_γ = ΔE_upper − ΔE_lower。
Count allowed transitions using the stated selection rules as well as the two level patterns.
根据所给的选择定则以及两个能级的模式来统计允许的跃迁。
Several transitions can share one frequency; the number of split states is not automatically the number of spectral lines.
多个跃迁可能共享同一频率；分裂态的数量并不自动等于谱线数量。
In a spin-neglected orbital model, an upper L equals 1 triplet has shifts m sub l mu sub B B with m sub l equals negative 1, 0, plus 1, and a lower L equals 0 state has zero shift.
在忽略自旋的轨道模型中，L = 1 的上三重态具有 m_l μ_B B 的位移，其中 m_l = −1, 0, +1，而 L = 0 的下能级状态位移为零。
Electric-dipole delta m sub l equals 0, plus or minus 1 permits three photon shifts negative mu sub B B, 0, plus mu sub B B.
电偶极子跃迁允许 Δm_l = 0, ±1，从而产生三种光子位移：−μ_B B、0、+μ_B B。
This normal-triplet model does not describe every real atom or fine-structure multiplet.
这种正常三重态模型并不能描述所有真实原子或精细结构多重态。
Polarisation and observation direction can change which components are detected.
偏振和观测方向可能会改变被检测到的成分。
In a uniform electric field F along z, an electron's perturbation is plus e F z for the stated electrostatic potential convention.
在沿z轴的均匀电场F中，根据所声明的静电势约定，电子的扰动为加eFz。
A nondegenerate parity eigenstate has angle z angle equals zero, so its first-order diagonal Stark shift vanishes, although a quadratic shift can remain.
非简并宇称本征态的⟨z⟩等于零，因此其一阶对角斯塔克位移消失，尽管二次位移可能仍然存在。
Exactly degenerate opposite-parity states instead allow an off-diagonal dipole matrix element.
完全简并的相反宇称态则允许出现非对角偶极矩阵元。
In an original two-state model, suppose the dipole matrix is open bracket open bracket zero comma d close bracket comma d comma zero close bracket close bracket, with real d in charge times length units.
在一个原始的两态模型中，假设偶极矩阵为 , ]，其中d为实数，单位为电荷乘长度。
The perturbation F times this matrix has eigenvalues plus minus d F and opposite superpositions of the two states.
扰动F乘以该矩阵的特征值为正负dF，以及两个状态的相反叠加。
Changing a basis phase changes the off-diagonal sign but not the splitting 2 absolute value of d F.
改变基矢相位会改变非对角项的符号，但不会改变分裂值2|dF|。
Actual near-degenerate atoms require comparison with fine structure and other small splittings before an exactly degenerate approximation is adopted; this supplied matrix is not a universal hydrogen coefficient.
实际的近简并原子在采用完全简并近似之前，需要与精细结构和其他小分裂进行比较；此提供的矩阵并非通用的氢原子系数。
In a weak field with LS coupling, label the states by J and m J, not by m l and m s.
在 LS 耦合的弱场中，用 J 和 mJ 而不是 ml 和 ms 来标记状态。
The shift is mu B B times g J times m J, where g J is one plus J times J plus 1, plus S times S plus 1, minus L times L plus 1, all over 2 J times J plus 1.
能移等于 μB B 乘 gJ 乘 mJ，其中 gJ 等于一加上 J(J+1) 加 S(S+1) 减 L(L+1)，再除以 2J(J+1)。
For L equal to 1, S one half and J three halves, g J is four thirds.
对于 L 等于 1、S 等于二分之一、J 等于二分之三，gJ 等于三分之四。
In a 2 tesla field, the m J equals one half sublevel moves up by 5.788 times 10 to the minus 5, times 2, times four thirds, times one half: 7.72 times 10 to the minus 5 electron volts.
在 2 特斯拉的磁场中，mJ 等于二分之一的子能级上移 5.788 乘 10 的负 5 次方，乘 2，乘三分之四，再乘二分之一：7.72 乘 10 的负 5 次方电子伏。
Photon shifts subtract the lower level's shift.
光子的移动要减去下能级的移动。
Two opposite-parity degenerate states have a dipole perturbation matrix with zero in the top-left position, d F in the top-right position, d F in the bottom-left position, and zero in the bottom-right position.
两个宇称相反的简并态具有偶极微扰矩阵，其左上角为零，右上角为 dF，左下角为 dF，右下角为零。
Find energies and eigenstates to first order.
求一阶能量本征值和本征态。
Compare with two such states separated by a large unperturbed gap Delta.
将其与两个由大未微扰能隙 Δ 分隔的此类状态进行比较。
Degenerate shifts are plus or minus d F, with eigenstates one plus or minus one, all over the square root of two.
简并移动为正负dF，本征态为一加一减一除以根号二。
Splitting is two times the absolute value of d F.
分裂为2倍|dF|。
With a large gap, each parity state's first-order diagonal shift is zero.
在大能隙下，每个宇称态的一阶对角移动为零。
Off-diagonal coupling instead gives ground shift approximately negative d F squared, all over delta.
非对角耦合则给出基态移动约等于负dF平方除以delta。
Award shifts, states, splitting, vanishing nondegenerate first order and quadratic correction condition.
评分点包括：移动、态、分裂、非简并一阶项消失及二次修正条件。
Declare the coupling regime, keep the negative electron moment sign, and subtract lower-level shifts.
声明耦合区域。 保留电子矩的负号。
Zero diagonal dipole expectation does not exclude degenerate mixing or quadratic shifts.
扣除低能级位移。 对角偶极期望值为零并不排除简并混合或二次位移。
Landé factor.
朗德因子。
This is a projection factor relating a weak-field LS-coupled magnetic shift to g sub J times m sub J.
这是一个投影因子，将弱场LS耦合磁位移与g下标J乘以m下标J联系起来。
Stark splitting.
斯塔克分裂。
This is an electric-field-induced separation of atomic energy levels, with symmetry and degeneracy controlling leading order.
这是由电场引起的原子能级分离，其对称性和简并度控制着主导阶效应。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
不阅读定义，直接回忆相关含义，然后在原始传递中改变一个参数，并检验极限情况。