[理学]CH1LEC2-结构化学.ppt

Chapter 1 Quantum Theory 1.1 Two Experiments 1.2 Wave nature of particles 1.3 Sch?dinger Equation 1.4 Some examples 1.3 Sch?dinger Equation 波函数 (Wavefunction ) 薛定谔方程 (Schr?dinger equation) 力学量和期望值 (Dynamic variables and expectation values) Born’s Interpretation of ? Max Born, 1926 ? corresponds to the square root of the probability density: The square root of the probability of finding a particle per unit volume. ? , however, may be a complex function. Differences Between Electronic Wavefunction and Electromagnetic Wavefunction 几率（probability): Differences Between Electronic Wavefunction and Electromagnetic Wavefunction Electromagnetic wavefunction(Plane wave): 描述电磁波某一时刻在空间某一位置的位相 Differences Between Electronic Wavefunction and Electromagnetic Wavefunction Shape of a plane wave at time t0 Differences Between Electronic Wavefunction and Electromagnetic Wavefunction 电子的波函数y(x,y,z,t)，应当描述电子某一时刻在空间某一位置出现的“几率”。特别地，当描述的体系为一个稳定的分子或原子时，电子在空间各处出现的几率将不随时间改变而改变。这样的状态成为“定态”。如不作特别说明，我们讨论的体系处于定态。上述波函数不符合作为电子波函数的要求。 Properties of ? Example: For some one-dimensional system, given state ?, wavefunction might be complex, However, the probability density must be real, Properties of ? 稳定系统y(x,y,z,t)应当具有的性质： Well behaved： Continuous and differentiable, single-valued, finite Normalized： Stationary state： Independent of time Normalization of Wavefunction Stationary State(定态） 定态是稳定的化学体系对波函数性质的进一步要求。保证电子在空间各处出现的几率不随时间的变化而改变。 稳定的原子或分子体系，电子即处于“定态”，而在化学反应过程中电子的运动状态就不能用定态波函数描述。 Equation of Motion Eigen-problem（本征问题） Equation of Motion Operators: Eigenfunction and eigenvalue: Equation of Motion Expectation Values of An Operator 如果f(x)不是算符 的本征函数，我们还是可以计算算符所对应的力学量的平均值(期望值)。 e.g. , 不是算符d/dx的本征函数,还是可以计算期望值 Equation of Motion 每一个力学量（Dynamic Variable) 都有与之对应的算符： Equation of Motion Schroedinger Equation for Hydrogen Atom 1.4 Simple