This Course Study Material is meant for use by M.Sc Students anywhere in India.

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This corresponds to a one semester first course in quantum mechanics.

It is assumed that the reader had an introduction to limitiations of classical theories and knows about old quantum theory developments such as Bohr Model, de Broglie Waves etc,

The course is divided into seven parts listed below.

Part-I | Rise of Wave Mechanics | |||

Overview | LectureNotes | Assignments | Lessons | |

Inadequacy of classical theories. Landmarks in rise of quantum theory. Review of classical and quantum particle and wave concepts. Uncertainty principle. The changes and new concepts brought in by quantum theory. Wave mechanics of a single point particle. | ||||

Part-II | Wave Mechanics of a Point Particles. | |||

Overview | Lecture Notes | |||

Optics and mechanics analogy. Time dependent Schrodinger equation. Conservation of probability. Interpretation of wave function as probability amplitude. Probability current density. Schrodinge equation for a charged particle. Time reversal. Free particle. Solution of time dependent Schrodinger equation for a free particle. Wave packets. Periodic boundary condition and box normalization. Free particle in two and three dimensions. Eigen-functions of momentum. Momentum space wave function. Quantum mechanics of a spin half particle. | ||||

Part-III | Motion of a Particle in a Potential Well. | |||

Overview | Lecture Notes | |||

Particle in a box. Boundary and matching conditions on wave function. Energy eigenvalues and eigenfunctions. Harmonic oscillator energy eigenvalues and eigen-functions. Periodic potential Reflection and transmission through a potential well. Barrier tunnelling. General properties of motion in one dimension. | ||||

Part-IV | Spherically Symmetric Potential Problems | |||

Overview | Lecture Notes | |||

Conservation of angular momentum. Reduction of two body central force problem to one body with reduced mass. Separation of variables in spherical polar coordinates. Solution of radial equation for free particle and piece wise constant potentials. Hydrogen atom energy levels and wave functions. Accidental degeneracy of Coulomb energy levels. | ||||

Part-V | General Principles of Quantum Mechanics | |||

Overview | Lecture Notes | |||

The structure of physical theories. Thought experiments and superposition principle in quantum mechanics. States and dynamical variables in quantum description of a physical system. Probability and average value. Canonical quantization. General form of uncertainty principle. Time evolution. Schrodinger, Heisenberg, and Dirac Pictures in quantum mechanics. Density matrix. Identical particles. | ||||

Part-VI | Matrix Mechanics | |||

Overview | Lecture Notes | |||

Harmonic oscillator energy levels. Angular momentum eigenvalues and eigenfunctions. | ||||

Part-VII | Working With Different Representations | |||

Overview | Lecture Notes | |||

Compatible variables. Commuting observables. Complete commuting set. Functions of operators and matrices. Simultaneous eigenvectors as basis in Hilbert space. State vectors as set of probability amplitudes. Examples. |

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The knowledge of vector spaces, linear operators etc is not required to get started.

It is needed only after Part-IV.

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