Preface
Acknowledgments
Author biography
1 Postulates
1.1 State space
1.2 Time evolution
1.3 Quantum measurement
1.4 Composite systems
1.5 The genie
Exercises
Bibliography
2 Two-state systems
2.1 Schrodinger's cat
2.2 Expectation value; energy operator
2.3 Spin one-half
2.3.1 Spin orientation measurements
2.3.2 Quantum mathematics of spin one-half
2.3.3 Spin precession
2.3.4 Heisenberg picture
2.4 Ammonia molecule
2.5 Photons
3 Entanglement
3.1 Entangled qubit pairs
3.2 Quantum gates
3.3 Utilizing entanglement
3.3.1 Superdense coding
3.3.2 Teleportation
3.3.3 Bell's inequality
3.4 Large-scale quantum algorithms
3.4.1 Classical algorithm for Simon's problem
3.4.2 Quantum algorithm for Simon's problem
Exercises
Bibliography
4 Quantum angular momentum
4.1 Operators for orbital angular momentum
4.2 Operators for spin one-half
4.3 Generalized angular momentum theory
4.4 Angular momentum addition
4.5 Interaction operators
4.6 Isospin
4.7 And
Exercises
Bibliography
5 Quantum many-body problem
5.1 The general case: Heisenberg XYZ spin chain
5.2 Ising model
5.3 Heisenberg XXX spin chain
5.3.1 N = 4 case: diagonalization
5.3.2 N = 4 case: Bethe ansatz
Exercises
Bibliography
6 Infinity, and beyond
6.1 Schrodinger equation
6.2 Schrodinger equation in one dimension
6.2.1 Free particle
6.2.2 Infinitely deep square well
6.2.3 Harmonic oscillator in one dimension
6.3 Schr6dinger equation in three dimensions
6.3.1 Free particle
6.3.2 Infinitely deep well
6.3.3 Harmonic oscillator
6.3.4 Spherically symmetric potentials
6.4 Defending the delta
Exercises
Bibliography
Appendix A Relevant results from linear algebra
Appendix B Directory of definitions and notation
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