PROOFS PROGRAMME

Quantum Mechanics-I (2018)

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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.

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  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.

 

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