文档介绍：QUANTUM MECHANICS
Professor John W. Norbury
Physics Department
University of Wisconsin-Milwaukee
. Box 413
Milwaukee, WI 53201
November 20, 2000
Contents
1 WAVE FUNCTION 7
Probability Theory ........................ 8
Mean, Average, Expectation Value ........... 8
Average of a Function .................. 10
Mean, Median, Mode .................. 10
Standard Deviation and Uncertainty .......... 11
Probability Density ................... 14
Postulates of Quantum Mechanics ............... 14
Conservation of Probability (Continuity Equation) ...... 19
Conservation of Charge ................. 19
Conservation of Probability ............... 22
Interpretation of the Wave Function .............. 23
Expectation Value in Quantum Mechanics ........... 24
Operators ............................. 24
Relations ..................... 27
Problems ............................. 32
Answers .............................. 33
2 DIFFERENTIAL EQUATIONS 35
Ordinary Di
erential Equations ................. 35
Second Order, Homogeneous, Linear, Ordinary Di
er-
ential Equations with Constant Coe
cients ...... 36
Inhomogeneous Equation ................ 39
Partial Di
erential Equations .................. 42
Properties of Separable Solutions ................ 44
General Solutions ..................... 44
Stationary States ..................... 44
De
nite Total Energy .................. 45
1
2 CONTENTS
Alternating Parity .................... 46
Nodes ........................... 46
Orthonormal Sets of Functions ....... 46
Time-dependent Coe
cients .............. 49
Problems ............................. 50
Answers .............................. 51
3 INFINITE 1-DIMENSIONAL BOX 53
Energy Levels ........................... 54
Wave Function ..............