Tính đối xứng hoán vị, cặp spin và nguyên lý loại trừ Pauli
GRE Subject Test · GRE Physics Chủ đề 38 6:16 Giọng đọc tiếng Anh · phụ đề tiếng Anh + 中文 được ghi trực tiếp
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Two electrons can share one spatial orbital, provided their combined space-and-spin state is antisymmetric.
两个电子可以共用一个空间轨道，只要它们的空间加自旋的总态是反对称的。
This topic builds symmetric and antisymmetric two-particle states, pairs them with spin singlets and triplets, and counts the allowed two-electron states.
本主题构造对称和反对称的双粒子态，把它们与自旋单态和三重态配对，并计算允许的双电子态数目。
For identical particles, exchanging every coordinate and spin label changes a fermionic total wavefunction by a minus sign and leaves a bosonic one unchanged.
对于全同粒子，交换所有坐标和自旋标签会使费米子总波函数改变符号，而玻色子波函数保持不变。
Mathematical slots one and two label arguments, not permanently distinguishable particles.
数学槽位一和二标记的是变量，而非永久可区分的粒子。
For two distinct orthonormal orbitals a and b, spatial combinations are Psi plus or minus equals a of one times b of two plus or minus b of one times a of two, all over the square root of two.
对于两个不同的正交归一轨道a和b，空间组合为Psi正负等于a(1)b(2)正负b(1)a(2)，除以根号二。
Orthogonality makes these combinations normalised and gives exchange eigenvalues plus or minus one.
正交性使这些组合归一化，并给出交换本征值正负一。
If the two orbitals are identical, the antisymmetric combination is identically zero and the displayed symmetric formula is not correctly normalised; the double-occupation spatial state is simply a of one times a of two.
若两个轨道相同，反对称组合恒为零，且显示的对称公式未正确归一化；双占据空间态即为a(1)a(2)。
Recheck normalization whenever orbitals or their overlaps change.
每当轨道或其重叠发生变化时，请重新检查归一化。
Two spin one-half particles have one singlet, with total spin zero, which is antisymmetric under exchange, and three triplets, with total spin one, which are symmetric.
两个自旋二分之一的粒子有一个总自旋为零的单态，它在交换下是反对称的；还有三个总自旋为一的三重态，它们是对称的。
Electrons need an antisymmetric total state, so symmetric space pairs with the singlet and antisymmetric space with a triplet.
电子要求总态反对称，所以对称的空间态与单态配对，反对称的空间态与三重态配对。
Two electrons in the same orbital can therefore form only the singlet.
因此两个电子处在同一轨道时只能形成单态。
Pauli exclusion forbids two electrons in the same complete state, spin included, not two in one orbital.
泡利不相容原理禁止两个电子处于同一个完整的态（包括自旋），而不是禁止一个轨道里有两个电子。
For two spatial orbitals, a and b, and two spin states each, there are four complete single-particle states.
对于两个空间轨道 a 和 b，每个轨道有两个自旋态，共有四个完整的单粒子态。
Two identical electrons have 4 choose 2, which is 6, occupation patterns; two double-occupation singlets, one different-orbital singlet, and three different-orbital triplets.
两个全同电子有从 4 个中选 2 个，即 6 种占据模式：两个双占据单态、一个不同轨道单态和三个不同轨道三重态。
For three spatial orbitals, there are six complete states and 6 choose 2, which is 15, patterns.
对于三个空间轨道，有六个完整态，以及从 6 个中选 2 个，即 15 种模式。
Counting ordered assignments overcounts identical particles.
按有序分配计数会重复计算全同粒子。
Spinless bosons in two orbitals instead have three occupations; both in a, one in each, or both in b.
无自旋玻色子在两个轨道中则有三种占据：都在 a、各占一个、都在 b。
These counts assume no additional energy restriction and the stated accessible single-particle states; restricting total energy or spin projection changes the allowed subset.
这些计数假设没有额外的能量限制，并以所给的可及单粒子态为准；限制总能量或自旋投影会改变允许的子集。
An antisymmetric spatial state satisfies Psi sub minus of x, x equals zero, so its joint position density vanishes on the coincidence line.
反对称空间态满足 Ψ_−(x,x) = 0，因此其联合位置密度在重合线上为零。
A symmetric spatial state need not vanish there.
对称空间态在该处不一定为零。
The difference arises from interference between exchanged amplitudes, even for noninteracting particles; it is not a separately imposed classical repulsive force.
这种差异源于交换振幅之间的干涉，即使对于非相互作用粒子也是如此；它并非额外施加的经典排斥力。
For a well of length L, choose a of x equals the square root of two over L, times sine of pi x over L. Choose b of x equals the square root of two over L, times sine of 2 pi x over L.
对于长度为 L 的势阱，选取 a(x) = √(2/L) sin(πx/L)，b(x) = √(2/L) sin(2πx/L)。
At x sub one equals L over 4 and x sub two equals 3 L over 4, the antisymmetric spatial amplitude is negative 2 over L and its density is 4 over L squared. The symmetric amplitude is zero.
当 x₁ = L/4 且 x₂ = 3L/4 时，反对称空间振幅为 −2/L，其密度为 4/L²；对称振幅为零。
These are joint probability densities per two lengths, not dimensionless probabilities at exact points.
这些是每两个长度的联合概率密度，而非精确点上的无量纲概率。
Physical spin compatibility still decides which total electronic state uses each spatial combination.
物理自旋兼容性仍决定哪个总电子态使用每种空间组合。
For two different orthonormal orbitals a and b, the symmetric and antisymmetric spatial states are a of 1, b of 2, plus or minus b of 1, a of 2, all over root 2.
对于两个不同的正交归一轨道 a 和 b，对称和反对称空间态为 a(1)b(2) 加或减 b(1)a(2)，再除以根号 2。
The total state must be antisymmetric under exchanging position and spin together.
总态在同时交换位置和自旋时必须反对称。
So symmetric space pairs with the singlet, and antisymmetric space with the triplet.
所以对称空间态与单态配对，反对称空间态与三重态配对。
Both electrons in a give a symmetric product, so only the singlet is allowed, and the root 2 factor no longer applies.
两个电子都在 a 时空间乘积是对称的，因此只允许单态，并且不再有根号 2 因子。
Two electrons access three orthonormal spatial orbitals, with no energy restriction.
两个电子占据三个正交归一的空间轨道，无能量限制。
Count singlet states and triplet states, including spin projections.
计算单重态和三重态的数量，包括自旋投影。
Reconcile the sum with choosing two complete states from six.
将总和与从六个完整状态中选取两个进行核对。
Five.
五分。
Symmetric spatial states: three double occupations plus three different-orbital symmetric pairs, giving six singlets.
对称空间态：三个双占据加上三个不同轨道的对称对，共给出六个单重态。
Antisymmetric space has three orbital pairs; each permits three triplet spin projections, giving nine triplet states.
反对称空间有三个轨道对；每个允许三个三重态自旋投影，共给出九个三重态。
Total is fifteen, equal to 6 choose 2.
总数为15，等于C(6,2)。
Award double occupations, singlet total, antisymmetric pairs, triplet total and reconciliation.
需指出双占据、单重态总数、反对称对、三重态总数及一致性验证。
Counting only the three triplet multiplets would omit their spin projections.
若仅计算三个三重态多重态，则会遗漏其自旋投影。
Exchange all spatial and spin arguments.
交换所有空间与自旋参量。
Do not confuse antisymmetric space with antisymmetric total state, or use the distinct-orbital square root of 2 factor for two identical orbitals.
切勿将反对称空间与反对称总态混淆，也不要在两个相同轨道的情形下使用区分轨道的根号2因子。
Spin singlet, 自旋单态, is the antisymmetric state of two spin-one-half particles with total spin S equal to zero.
自旋单态：两个自旋二分之一粒子的反对称态，总自旋 S 等于零。
Slater determinant, 斯莱特行列式, is the antisymmetric fermionic construction from complete single-particle states; duplicate states make it vanish.
斯莱特行列式：由完整单粒子态构成的反对称费米子构造；出现重复的态时行列式为零。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
在不阅读定义的情况下回忆其含义，然后改变原始传递中的一个参数，并检验极限情况。