Quantum Mechanics Made Simple: Lecture Notes

1 Quantum Mechanics Made Simple: Lecture NotesWeng Cho CHEW1 October 5, 20121 The author is with U of Illinois, Urbana-Champaign. He works part time at Hong Kong U Introduction .. Quantum Mechanics is Bizarre .. The Wave Nature of a Particle Wave Particle Duality ..22 Classical Introduction .. Lagrangian Formulation .. Hamiltonian Formulation .. More on Hamiltonian .. Poisson Bracket ..123 Quantum Mechanics Some Introduction .. Probabilistic Interpretation of the wavefunction.

2 Simple Examples of Time Independent Schr odinger Equation .. in a 1D Box .. Scattering by a Barrier .. in a Potential Well .. The Quantum Harmonic Oscillator ..234 Time-Dependent Schr odinger Introduction .. Quantum States in the Time Domain .. Coherent State .. Measurement Hypothesis and Expectation Value .. Evolution of the Hamiltonian Operator .. Principle .. Current ..32iiiQuantum Mechanics Made Simple5 Mathematical A Function is a Vector.

3 Operators .. Representation of an Operator .. Expansion of an Operator .. of an Operator .. Operators .. Operators .. Identity Operator in a Continuum Space .. Changing Between Representations .. Coordinate Basis Function .. Commutation of Operators .. Expectation Value and Eigenvalue of Operators .. Generalized Uncertainty Principle .. Time Evolution of the Expectation Value of an Operator .. Periodic Boundary Condition ..546 Approximate Methods in Quantum Introduction.

4 Use of an Approximate Subspace .. Time Independent Perturbation Theory .. Tight Binding Model .. Method .. Dependent Perturbation Theory ..677 Quantum Mechanics in Introduction .. Bloch-Floquet Waves .. Bloch-Floquet Theorem for 3D .. Effective Mass Schr odinger Equation .. Density of States (DOS) .. DOS in a Quantum Well ..818 Angular Introduction .. Trapped in a Pill Box .. Trapped in a Spherical Box .. Mathematics of Angular Momentum.

5 L2 Operator ..92 Contentsiii9 Introduction .. Spin Operators .. The Bloch Sphere .. Spinor .. Pauli Equation ..9910 Identical Introduction .. Pauli Exclusion Principle .. Exchange Energy .. Extension to More Than Two Particles .. Counting the Number of Basis states .. Examples .. Thermal Distribution Functions .. 10711 Density Pure and Mixed States .. Density Operator .. Time Evolution of the Matrix Element of an Operator.

6 Interaction of Light with Two-Level Atomic System .. 11512 Quantization of Classical Introduction .. The Quantum Harmonic Oscillator Revisited .. Eigenfunction by the Ladder Approach .. Quantization of Waves on a Linear Atomic Chain Phonons .. Schr odinger Picture versus Heisenberg Picture .. The Continuum Limit .. Quantization of Electromagnetic Field .. Hamiltonian .. Field Operators .. Multimode Case and Fock State .. One-Photon State.

7 Coherent State Revisited .. 14113 Schr odinger Wave Introduction .. Fock Space for Fermions .. Field Operators .. Similarity Transform .. Additive One-Particle Operator .. Three-Particle Case .. Additive Two-Particle Operator .. More on Field Operators .. 155ivQuantum Mechanics Made Boson Wave Field .. Boson Field Operators .. One-Particle Operator .. Difference between Boson Field and Photon Field .. 16014 Interaction of Different Introduction.

8 Interaction of Particles .. Time-Dependent Perturbation Theory .. Absorption .. Spontaneous Emission .. Stimulated Emission .. Multi-photon Case .. Total Spontaneous Emission Rate .. 16715 Quantum Information and Quantum Introduction .. Quantum Cryptography .. No-cloning Theorem .. Entangled States .. A Simple Quantum Encryption Algorithm.. Quantum Computing .. Quantum Bits (Qubits) .. Quantum Gates.

9 Quantum Computing Algorithms .. Quantum Teleportation .. Interpretation of Quantum Mechanics .. EPR Paradox .. Bell s Theorem .. Prediction by Quantum Mechanics .. Prediction by Hidden Variable Theory .. A Final Word on Quantum Parallelism .. 187A Generators of Translator and Infinitesimal Translation .. Infinitesimal Rotation .. Derivation of Commutation Relations .. 193B Quantum Statistical Introduction .. Distinguishable Particles.

10 Identical Fermions .. Identical Bosons .. Most Probable Configuration .. Distinguishable Particles .. Identical Fermions .. Identical Bosons .. The Meaning of and .. 200C Gaussian Wave Introduction .. Derivation from the Wave Equation .. Physical Interpretation .. Stability of the Plane Wave Solution .. 207viQuantum Mechanics Made SimplePrefaceThis set of supplementary Lecture Notes is the outgrowth of a course I taught, ECE 487, Quantum Electronics, at ECE Department, University of Illinois at Urbana-Champaign.