Quantum Mechanics Demystified Book

	Preface	ix
	Acknowledgments	xi
Chapter 1	Historical Review	1
	Blackbody Radiation and Planck's Formula	1
	The Photoelectric Effect	6
	The Bohr Theory of the Atom	7
	de Broglie's Hypothesis	10
	Quiz	11
Chapter 2	Basic Developments	13
	The Schrodinger Equation	13
	Solving the Schrodinger Equation	18
	The Probability Interpretation and Normalization	24
	Expansion of the Wavefunction and Finding Coefficients	35
	The Phase of a Wavefunction	44
	Operators in Quantum Mechanics	46
	Momentum and the Uncertainty Principle	54
	The Conservation of Probability	59
	Quiz	63
Chapter 3	The Time Independent Schrodinger Equation	65
	The Free Particle	66
	Bound States and 1-D Scattering	74
	Parity	88
	Ehrenfest Theorem	95
	Quiz	96
Chapter 4	An Introduction to State Space	99
	Basic Definitions	99
	Hilbert Space Definitions	100
	Quiz	110
Chapter 5	The Mathematical Structure of Quantum Mechanics I	111
	Linear Vector Spaces	111
	Basis Vectors	122
	Expanding a Vector in Terms of a Basis	124
	Orthonormal Sets and the Gram-Schmidt Procedure	124
	Dirac Algebra with Bras and Kets	125
	Finding the Expansion Coefficients in the Representation of Bras and Kets	127
	Quiz	129
Chapter 6	The Mathematical Structure of Quantum Mechanics II	131
	The Representation of an Operator	133
	Eigenvalues and Eigenvectors	142
	The Hermitian Conjugate of an Operator	152
	The Commutator	167
	Quiz	172
Chapter 7	The Mathematical Structure of Quantum Mechanics III	175
	Change of Basis and Unitary Transformations	175
	The Generalized Uncertainty Relation	185
	Projection Operators	188
	Functions of Operators	193
	Generalization to Continuous Spaces	194
	Quiz	203
Chapter 8	The Foundations of Quantum Mechanics	205
	The Postulates of Quantum Mechanics	205
	Spectral Decomposition	209
	Projective Measurements	211
	The Completeness Relation	212
	Completely Specifying a State with a CSCO	220
	The Heisenberg versus Schrodinger Pictures	221
	Describing Composite Systems in Quantum Mechanics	222
	The Matrix Representation of a Tensor Product	223
	The Tensor Product of State Vectors	224
	The Density Operator	226
	The Density Operator for a Completely Mixed State	229
	A Brief Introduction to the Bloch Vector	237
	Quiz	239
Chapter 9	The Harmonic Oscillator	241
	The Solution of the Harmonic Oscillator in the Position Representation	241
	The Operator Method for the Harmonic Oscillator	250
	Number States of the Harmonic Oscillator	253
	More on the Action of the Raising and Lowering Operators	256
	Quiz	258
Chapter 10	Angular Momentum	259
	The Commutation Relations of Angular Momentum	260
	The Uncertainty Relations for Angular Momentum	262
	Generalized Angular Momentum and the Ladder Operators	262
	Matrix Representations of Angular Momentum	272
	Coordinate Representation of Orbital Angular Momentum and the Spherical Harmonics	283
	Quiz	293
Chapter 11	Spin-1/2 Systems	295
	The Stern-Gerlach Experiment	296
	The Basis States for Spin-1/2 Systems	298
	Using the Ladder Operators to Construct S[subscript x], S[subscript y]	300
	Unitary Transformations for Spin-1/2 Systems	308
	The Outer Product Representation of the Spin Operators	310
	The Pauli Matrices	312
	The Time Evolution of Spin-1/2 States	317
	The Density Operator for Spin-1/2 Systems	328
	Quiz	329
Chapter 12	Quantum Mechanics in Three Dimensions	331
	The 2-D Square Well	332
	An Overview of a Particle in a Central Potential	341
	An Overview of the Hydrogen Atom	342
	Quiz	356
	Final Exam	357
	Answers to Quiz and Exam Questions	363
	References	385
	Index	387