剪切稀化（假塑性）

A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is characterized by a yield stress, [latex]\tau_0[/latex], which is the minimum shear stress required to initiate flow. Below this threshold, it does not deform. Common examples include toothpaste, mayonnaise, and clay slurries.

This is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. It is a linear partial differential equation for the wavefunction, [latex]\Psi(x, t)[/latex]. The time-dependent version is [latex]i\hbar\frac{\partial}{\partial t}\Psi = \hat{H}\Psi[/latex], where [latex]\hat{H}[/latex] is the Hamiltonian operator, representing the total energy of the system.

In quantum mechanics, momentum is an observable represented by a vector operator. In the position basis, the momentum operator is given by [latex]\hat{\vec{p}} = -i\hbar\nabla[/latex], where [latex]\hbar[/latex] is the reduced Planck constant and [latex]\nabla[/latex] is the gradient operator. The conservation of momentum corresponds to the fact that the Hamiltonian operator commutes with the momentum operator, [latex][\hat{H}, \hat{\vec{p}}] = 0[/latex], for a system with translational symmetry.

It is impossible to simultaneously know with perfect accuracy certain pairs of complementary physical properties of a particle. The most common example is the position [latex]x[/latex] and momentum [latex]p[/latex]. The principle states that the product of their uncertainties, [latex]\Delta x[/latex] and [latex]\Delta p[/latex], must be greater than or equal to a specific value: [latex]\Delta x \Delta p \ge \frac{\hbar}{2}[/latex].

自催化是一种化学反应，其中一种反应产物同时也是同一反应或偶联反应的催化剂。这形成了一个正反馈回路，导致反应速率加快。反应速率最初较慢，但随着产物（催化剂）浓度的增加而加快，通常形成S形动力学曲线。

The Landé g-factor ([latex]g_J[/latex]) is a dimensionless proportionality constant that relates an atom's total magnetic moment to its total angular momentum in the weak-field limit. It is crucial for quantitatively explaining the anomalous Zeeman effect. Its value is given by the formula: [latex]g_J = 1 + \frac{J(J+1) + S(S+1) - L(L+1)}{2J(J+1)}[/latex], where L, S, and J are the quantum numbers.

All quantum entities, such as photons and electrons, exhibit both particle and wave properties. Depending on the experimental setup, they can behave like a localized particle or a distributed wave. The de Broglie hypothesis states that any particle with momentum [latex]p[/latex] has an associated wavelength [latex]\lambda = h/p[/latex], where [latex]h[/latex] is Planck's constant.

pH is formally defined as the negative decimal logarithm of the hydrogen ion activity, [latex]a_{H^+}[/latex]. The formula is [latex]pH = -\log_{10}(a_{H^+})[/latex]. Activity is the effective concentration of hydrogen ions, accounting for intermolecular forces, and is dimensionless. For dilute solutions, activity is approximately equal to the molar concentration of [latex]H^+[/latex] ions, simplifying the calculation.

镧系收缩是指镧系元素（从镧到镥）的原子半径和离子半径随着原子序数的增加而逐渐减小的现象。这种效应是由于4f电子对核电荷的屏蔽作用较弱造成的。这导致镧系元素之后的第六周期元素意外地小，与第五周期元素相似。

Quantum statistics modifies classical statistical mechanics to account for the indistinguishability of identical particles. It splits into two types: Fermi-Dirac statistics for fermions (half-integer spin particles like electrons), which obey the Pauli exclusion principle, and Bose-Einstein statistics for bosons (integer spin particles like photons), which can occupy the same quantum state. This distinction is crucial at low temperatures and high densities.

触变性和流变性描述的是粘度随时间的变化。触变性流体的粘度在恒定的剪切应力下会随时间降低（例如，酸奶在搅拌时会变得更稀）。流变性（或抗触变性）流体的粘度在恒定的剪切应力下会随时间增加（例如，某些润滑剂）。这些效应是可逆的；流体在静置一段时间后会恢复到原始状态。

A quantum mechanical phenomenon where a wavefunction can propagate through a potential energy barrier. Classically, a particle lacking sufficient energy to surmount a barrier would be reflected. However, due to the wave-like nature of particles, there is a non-zero probability that the particle can appear on the other side of the barrier, effectively 'tunneling' through it.