2.Keypoints and Difficulties Keypoints:One-Dimensional Schrodinger Equation;Potential Wells:The Harmonic Oscillator Difficulties:Potential Wells:The Harmonic 0scillator 3.Contents 4.1 Wave Functions and the One-Dimensional Schrodinger Equation 4.2 Particle in a Box 4.3 Potential Wells 4.4 Potential Barriers and Tunneling 4.5 The Harmonic Oscillator 4.Teaching method Teaching:Group Discussion:Autodidacticism under the guidance of the teacher 5.Comments Carefully prepare lessons,prepare students and make preparations before class:In the teaching process,we pay attention to cultivating students'creative thinking,take students as the main body and enhance students'sense of participation:Corresponding exercises and supplementary exercises after class. Problems: 1.An electron is moving as a free particle in the x-direction with momentum that has magnitude 4.50*10 kg.m/s.What is the one- dimensional time-dependent wave function of the electron? 2. Ground-Level Billiards.(a)Find the lowest energy level for a particle in a box if the particle is a billiard ball (m-=0.20 kg)and the box has a width of 1.3 m,the size of a billiard table.(Assume that the billiard ball slides without friction rather than rolls:that is,ign the rotational kinetic energy.)(b)Since the energy in part (a)is all kinetic,to what speed does this correspond?How much time would it take at this speed for the ball to move from one side of the table to the other?(c)What is the difference in energy between the n=2 and n=1 levels?(d)Are quantum-mechanical effects important for the game of billiards? 3. An electron is bound in a square well with a depth equal to six times the ground-level energy El-IDW of an infinite well of the same 2. Keypoints and Difficulties Keypoints: One-Dimensional Schrödinger Equation; Potential Wells; The Harmonic Oscillator Difficulties: Potential Wells; The Harmonic Oscillator 3. Contents 4.1 Wave Functions and the One-Dimensional Schrödinger Equation 4.2 Particle in a Box 4.3 Potential Wells 4.4 Potential Barriers and Tunneling 4.5 The Harmonic Oscillator 4. Teaching method Teaching; Group Discussion; Autodidacticism under the guidance of the teacher 5. Comments Carefully prepare lessons, prepare students and make preparations before class; In the teaching process, we pay attention to cultivating students' creative thinking, take students as the main body and enhance students' sense of participation; Corresponding exercises and supplementary exercises after class. Problems: 1. An electron is moving as a free particle in the x-direction with momentum that has magnitude 4.50*10-24 kg﹒m/s. What is the one￾dimensional time-dependent wave function of the electron? 2. Ground-Level Billiards. (a) Find the lowest energy level for a particle in a box if the particle is a billiard ball (m=0.20 kg) and the box has a width of 1.3 m, the size of a billiard table. (Assume that the billiard ball slides without friction rather than rolls; that is, ignore the rotational kinetic energy.) (b) Since the energy in part (a) is all kinetic, to what speed does this correspond? How much time would it take at this speed for the ball to move from one side of the table to the other? (c) What is the difference in energy between the n=2 and n=1 levels? (d) Are quantum-mechanical effects important for the game of billiards? 3. An electron is bound in a square well with a depth equal to six times the ground-level energy E1-IDW of an infinite well of the same