PH5007: Quantum Mechanics 1

L-T-P-C: 3-1-0-4

Prerequisites: None

Syllabus

Module 1: Origin of quantum theory

( Lecture hours: 3 , Tutorial hours: 0 , Lab hours: 0 )

Basic principles of quantum mechanics .

Module 2: Linear Algebra

( Lecture hours: 7 , Tutorial hours: 3 , Lab hours: 0 )

Linear vector spaces, Bra and ket vectors, Inner products, Hilbert space, Operators, Completeness and orthonormality, Basis sets and change of basis, Eigenstates and eigenvalues, Wave-functions, Expectation values, Uncertainty relation, Position and momentum representations .

Module 3: Hilbert space formulation of quantum mechanics

( Lecture hours: 5 , Tutorial hours: 2 , Lab hours: 0 )

States, observables and measurement, Discrete and continuous spectra, Wavefunctions in position and momentum space .

Module 4: Dynamics

( Lecture hours: 5 , Tutorial hours: 2 , Lab hours: 0 )

Time evolution, Hamiltonian, Schrodinger equation, Schrodinger and Heisenberg picture, Probability current .

Module 5: Simple 1D Examples

( Lecture hours: 7 , Tutorial hours: 2 , Lab hours: 0 )

Particle in a box, Delta function, Finite well and potential barriers, Bound states and scattering, Harmonic oscillator: wavefunction and operator approach .

Module 6: Symmetries in Quantum Mechanics

( Lecture hours: 5 , Tutorial hours: 2 , Lab hours: 0 )

Discrete symmetries, Translation, Parity, Time reversal, Rotational symmetry .

Module 7: Hydrogen atom

( Lecture hours: 8 , Tutorial hours: 2 , Lab hours: 0 )

Orbital angular momentum operators, Operator and wave function approach, Spherical harmonics, Fine and hyperfine structure of H atom .

Module 8: Systems of identical particles

( Lecture hours: 2 , Tutorial hours: 1 , Lab hours: 0 )

Permutation symmetry, Symmetric and antisymmetric wavefunctions, Bosons and Fermions, Pauli's exclusion principle .

Study Materials

Textbooks

  1. Modern Quantum Mechanics, J. J. Sakurai, Addison Wesley; Revised Edition, ISBN: 978-0201539295
  2. Introduction to Quantum Mechanics, David J. Griffiths, Pearson Education; 2nd Edition, ISBN: 978-9332542891

References

  1. Principles of Quantum Mechanics, R. Shankar, Springer; 2nd Edition, ISBN: 978-0306447907
  2. Quantum Mechanics, C. Cohen Tannoudji, Bernard Diu, Frank Laloe, Wiley-VCH, ISBN: 978-0471569527
  3. Quantum Mechanics, Eugene Merzbacher, Wiley; 3rd Edition, ISBN: 978-8126533176
  4. Lectures on Quantum Mechanics, Steven Weinberg, Cambridge University Press; 2nd Edition, ISBN: 978-1316276105
  5. Quantum Mechanics, V. K. Thankappan, New Academic Science Ltd; 4th Revised Edition, ISBN: 978-1781830147