Introduction to Quantum Mechanics
(Spring 1998)
Instructor: T.-M. Lu
Section I: (Chapter 1)
Review of Classical Mechanics
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Newtonian mechanics
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Coordinate transformations
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Lagrangian approach
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Hamiltonian with generalized momenta
Section II: (Chapter 2)
Review of Quantum Physics
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wave nature of particles
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Schroedinger Equation
Section III: (Chapter 3)
Postulates of Quantum Mechanics
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Postulate I
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Postulate II
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Postulate III
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Postulate IV
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Formal solution of Schroedinger Equation
Section IV: (Chapter 4)
Mathematical Foundation-A
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Eigenstates: particle in a box
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Dirac notation
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Hilbert space
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Hermitian operators
Section V: (Chapters 5 and 6)
Mathematical Foundation-B
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Mixed states
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Commutators and commuting operators
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Degeneracy
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Time dependent expectation values
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Conservation laws
Section VI: (Chapter 7)
Creation and annihilation operators
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Creation and annihilation operators
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Eigenvalues of harmonic oscillator
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Eigenfunctions of harmonic oscillator
Section VII: (Chapter 9)
Ladder operators
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Ladder operator
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Eigenvalues of angular momentum
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Eigenfunctions of angular momentum
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Addition of angular momenta
Section VIII: (Chapter 11)
Matrix mechanics
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Basis and representations
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Matrix operation
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Diagonalization of operators
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Spin and spin matrices
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