医学物理学chapter 10c_13.ppt

Summary to the last lecture 10.7 The Heisenberg Uncertainty principle 10.8 Schr?dinger equation 10.8.1 The interpretation of wave function 10.8.2 Schr?dinger equation 10.8.3 one-dimensional infinite deep potential well 10.8.4 The tunneling effect (隧道效应) equation of motion Velocity and the position of a particle in a particular moment can be found Quantum mechanics Wave function to describe the motion of particles (?) What does the wave function mean? Newtonian mechanics The wave function ?(x,y,z,t) for a particle contains all information about the particle. Two questions that immediately arise: First, what is the meaning of the wave function ? for a particle? Second, how is ? to be determined for any given physical situation? Answer to question 1: Wave function can describes The distribution, the probability, charge density at any point in space. In addition, from ? one can calculate the average position of the particle, its average velocity, and dynamic quantities such as momentum, energy, and angular momentum. The answer to the second question: wave function must be one of a set of solutions of Schr?dinger equation, developed by Schr?dinger in 1925. set up a Schr?dinger equation for any given physical situation, such as electron in hydrogen atom; the functions that are solutions of this equation represent the various possible physical states of the system. The precise interpretation of the wave function is given by M Born in 1926. He pointed out a statistical explanations for the wave functions (1) the wave function ? is a probability wave function. | ? |2 = ?·?* is the density of probability, |?(x)|2 dx 1954 Nobel Prize (2) the wave functions have to be satisfied with the standard conditions of single value, continuity and finite. (3) the wave functions should be normalized, This is called normalizing condition. It means that at a particular time, the probability of finding the particle in the whole space is equal to 1 (100%). (9.7.1) (4) The wa