Quantum Mechanics-I A course given at University of Hyderabad Summer Semester May14 - July10 (2018) |

This course aims to introduce wave mechanics with minimal mathematics preparation. No vector spaces are required as prerequisite.

The postulates are adopted for a wave mechanical treatment ofa single particle moving in a potential. Formal vector spaces and abstract approach can be taken up at a later stage of learning.

This course is suitable for those who want to come to Schrodinger equation and applications as quickly as possible.

This course will consist of following parts.

### Part-A Rise of Quantum Theory

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-B Wave Mechanics of a Point Particle

Optics and mechanics analogy.

Time dependent Schrodinger equation. Conservation of probability.

Interpretation of wave function as probability amplitude. Probability

current density. Schrodinger 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.

Eigenfunctions of momentum. Momentum space wave function. Quantum mechanics

of a spin half particle.

### Part-C Motion of a particle in potential well

Particle in a box. Boundary and matching conditions on wave function. Energy

eigenvalues and eigenfunctions. Harmonic oscillator energy eigenvalues and

eigenfunctions. Periodic potential

Reflection and transmission through a potential well. Barrier tunnelling.

General properties of motion in one dimension.

### Part-D Spherically symmetric potentials in three dimensions

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-E General principles of quantum mechanics

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-F Working with representations

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.

Coordinate and momentum representations as examples. Spin matrices and their

properties. Wave function of a particle with spin.

### Part-G Matrix mechanics

Harmonic oscillator energy levels. Angular momentum eigenvalues and

eigenfunctions. Addition of angular momenta

### Part-I Approximatin Schemes

Time independent first order perturbation theory non degenerate

and degenerate levels. Second order corrections for non degenerate levels.

Rayleigh Ritz Variation method. WKB apprximation.

### Tutorial, Quiz, Test and Examination Papers