《--ch01wavefunctionandschrodingerequation1-1-wm》由会员分享，可在线阅读，更多相关《--ch01wavefunctionandschrodingerequation1-1-wm（20页珍藏版）》请在金锄头文库上搜索。
1、Ch1 Wave Function & SE Ch 1 Wave Function & SchrCh 1 Wave Function & Schr dinger Equationdinger EquationTwo postulationsTwo postulations：A.A. Wave function describes the behavior of Wave function describes the behavior of particles. Wave function has probability particles. Wave function has probabil
2、ity property.property.B.B. Wave function will be solving by Wave function will be solving by SchrSchr dinger Equation.dinger Equation.Mainly on:Mainly on:Ch1 Wave Function & SE1). Wave Function1). Wave Function)(2cos)(cos00 xtuxt=Drop off the imaginary partDrop off the imaginary partEuler Euler s fo
3、rmulas formula sincosiei+ += =In 3 dimensionIn 3 dimension 1.1 The statistical Interpretation of Wave Function1.1 The statistical Interpretation of Wave Function)(0),(xpEti xetx= =h ),(),(tzyxtr = =rCh1 Wave Function & SE1). Wave Function1). Wave Function quantum state of particlequantum state of pa
4、rticle amplitude of probabilityamplitude of probabilityPhysical Significance:Physical Significance:Probability of finding the particle Probability of finding the particle at at r r, at time , at time t t, per volume , per volume - - probability densityprobability density matter wave matter wave prob
5、ability wave Max Born probability wave Max Born IdeaIdea probability probability weight average weight average physical observablephysical observablewhere where * * is the complex conjugate (c.c. in short) of is the complex conjugate (c.c. in short) of . .( (e eiaia) ) * *=?=? 1.1 The statistical In
6、terpretation of Wave Function1.1 The statistical Interpretation of Wave Function),(),(tzyxtr = =r*2),(=trrCh1 Wave Function & SE2). Concepts of Probability Wave (at time 2). Concepts of Probability Wave (at time t t) )probability density, PD in shortprobability density, PD in short probability distr
7、ibution functionprobability distribution functionA.A.B.B.probability of finding the particle probability of finding the particle in volume element (in volume element (r r, , r r+d+dr r) )C.C.normalizationnormalizationIntroduceIntroduce Thus (Thus ( , , ) = 1) = 1QuestionsQuestionsd d 3 3r r =? ( =?
8、( , , ) = ?) = ? 1.1 The statistical Interpretation of Wave Function1.1 The statistical Interpretation of Wave Function2)(rv rdr32)(v 1)(32= = rdrr = *d），（），（Ch1 Wave Function & SE2). Concepts of Probability Wave (at time t)2). Concepts of Probability Wave (at time t)relative probabilityrelative pro
9、babilityD.D.QuestionQuestionDo Do ( (r r) and ) and C C ( (r r) describe the same ) describe the same quantum state ?quantum state ?uncertain constantuncertain constantQuestionQuestionIn classical physics, are In classical physics, are ( (r r) and ) and C C ( (r r) ) the same?the same?Intensity of w
10、ave Intensity of wave | | C C ( (r r) |) |2 2Not the sameNot the same 1.1 The statistical Interpretation of Wave Function1.1 The statistical Interpretation of Wave Function221221 )()( )()( rr rCrCrr rr = =Ch1 Wave Function & SE2). Concepts of Probability Wave (at time t)2). Concepts of Probability W
11、ave (at time t) E.E.QuestionQuestionDo Do ( (r r) and ) and ( (r r) )e ei i describe the describe the same quantum state ?same quantum state ?uncertain phaseuncertain phaseIn classical physics, In classical physics, ( (r r) and ) and ( (r r) ) e ei i are not are not the same. Because the phase will
12、affect the the same. Because the phase will affect the result of interference of waves.result of interference of waves.They are the sameThey are the same 1.1 The statistical Interpretation of Wave Function1.1 The statistical Interpretation of Wave Functioniiiererer =*2)()()(rrr20*)()()(rerrrrr=Ch1 W
13、ave Function & SE2). Concepts of Probability Wave (at time t)2). Concepts of Probability Wave (at time t) F.F.If If ( (r r) is not normalized, we have,) is not normalized, we have,Normalization factorNormalization factorA1is called a normalization factoris called a normalization factorNormalizing a
14、wave function is to find the Normalizing a wave function is to find the normalization factor.normalization factor. 1.1 The statistical Interpretation of Wave Function1.1 The statistical Interpretation of Wave Function1)(1)(32 32= rdrAArdrrrCh1 Wave Function & SEPage 8: Page 8: 练习题练习题练习题练习题1 1： 高斯积分高
15、斯积分高斯积分高斯积分Gaussian IntegralGaussian Integral练习题练习题练习题练习题2 2： PD = constant, normalization?PD = constant, normalization?练习题练习题练习题练习题3 3： See page 243See page 243练习题练习题练习题练习题4 4：ExercisesExercises = = dxex2Ch1 Wave Function & SEYes. Reason:Yes. Reason:Can we use Can we use ( (p,tp,t) ) to describe the probability?to describe the probability? p p is corresponding to a monochrome is corresponding
